Trigonometry word problems with solutions are much useful to the kids who would like to practice problems on triangles in trigonometry.

Now, let us look at some trigonometry word problems with solutions.

**Problem 1 : **

The angle of elevation of the top of the building at a distance of 50 m from its foot on a horizontal plane is found to be 60 degree. Find the height of the building.

**Solution :**

First let us draw a figure for the information given in the question.

Here, AB represents height of the building, BC represents distance of the building from the point of observation.

In the right triangle ABC, the side which is opposite to the angle 60 degree is known as opposite side (AB), the side which is opposite to 90 degree is called hypotenuse side (AC) and the remaining side is called adjacent side (BC).

Now we need to find the length of the side AB.

tanθ = Opposite side/Adjacent side

tan 60° = AB/BC

√3 = AB/50

√3 x 50 = AB

AB = 50√3

Approximate value of √3 is 1.732

AB = 50 (1.732)

AB = 86.6 m

**Hence, the height of the building is 86.6 m**

Let us look at the next problem on "Trigonometry word problems with solutions"

**Problem 2 : **

A ladder placed against a wall such that it reaches the top of the wall of height 6 m and the ladder is inclined at an angle of 60 degree. Find how far the ladder is from the foot of the wall.

**Solution :**

First let us draw a figure for the information given in the question.

Here AB represents height of the wall, BC represents the distance between the wall and the foot of the ladder and AC represents the length of the ladder.

In the right triangle ABC, the side which is opposite to angle 60 degree is known as opposite side (AB), the side which is opposite to 90 degree is called hypotenuse side (AC) and remaining side is called adjacent side (BC).

Now we need to find the distance between foot of the ladder and the wall. That is, we have to find the length of BC.

tan θ = Opposite side/Adjacent side

tan60° = AB/BC

√3 = 6/BC

BC = 6/√3

BC = (6/√3) x (√3/√3)

BC = (6√3)/3

BC = 2√3

Approximate value of √3 is 1.732

BC = 2 (1.732)

BC = 3.464 m

**Hence, the distance between foot of the ladder and the wall is 3.464 m**

**Let us look at the next problem on "Trigonometry word problems with solutions"**

**Problem 3 : **

A string of a kite is 100 meters long and it makes an angle of 60° with horizontal. Find the height of the kite,assuming that there is no slack in the string.

**Solution :**

First let us draw a figure for the information given in the question.

Here AB represents height of kite from the ground, BC represents the distance of kite from the point of observation.

In the right triangle ABC the side which is opposite to angle 60 degree is known as opposite side (AB), the side which is opposite to 90 degree is called hypotenuse side (AC) and remaining side is called adjacent side (BC).

Now we need to find the height of the side AB.

Sin θ = Opposite side/Hypotenuse side

Sinθ = AB/AC

Sin 60° = AB/100

√3/2 = AB/100

(√3/2) x 100 = AB

AB = 50 √3 m

**Hence, the height of kite from the ground 50 √3 m**

**Let us look at the next problem on "Trigonometry word problems with solutions"**

**Problem 4 : **

From the top of the tower 30m height a man is observing the base of a tree at an angle of depression measuring 30 degree. Find the distance between the tree and the tower.

**Solution :**

First let us draw a figure for the information given in the question.

Here AB represents height of the tower, BC represents the distance between foot of the tower and the foot of the tree.

In the right triangle ABC the side which is opposite to the angle 30 degree is known as opposite side (BC), the side which is opposite to 90 degree is called hypotenuse side (AC) and the remaining side is called adjacent side (AB).

Now we need to find the distance between foot of the tower and the foot of the tree (BC).

tan θ = Opposite side/Adjacent side

tan30° = BC/AB

1/√3 = BC/30

30 = BC x √3

BC = (30/√3) x (√3/√3)

BC = (30√3)/3

BC = 10√3

Approximate value of √3 is 1.732

BC = 10 (1.732)

BC = 17.32 m

**Hence, the distance between the tree and the tower is 17.32 m**

**Let us look at the next problem on "Trigonometry word problems with solutions"**

**Problem 5 : **

A man wants to determine the height of a light house. He measured the angle at A and found that tan A = 3/4. What is the height of the light house if A is 40 m from the base?

**Solution :**

First let us draw a figure for the information given in the question.

Here BC represents height of the light house, AB represents the distance between the light house from the point of observation.

In the right triangle ABC the side which is opposite to the angle A is known as opposite side (BC), the side which is opposite to 90 degree is called hypotenuse side (AC) and remaining side is called adjacent side (AB).

Now we need to find the height of the light house (BC).

tanA = Opposite side/Adjacent side

tanA = BC/AB

Given : tanA = 3/4

3/4 = BC/40

3 x 40 = BC x 4

BC = (3 x 40)/4

BC = (3 x 10)

BC = 30 m

**Hence, the height of the light house is 30 m**

**Let us look at the next problem on "Trigonometry word problems with solutions"**

**Problem 6 : **

A man wants to determine the height of a light house. He A ladder is leaning against a vertical wall makes an angle of 20° with the ground. The foot of the ladder is 3 m from the wall.Find the length of ladder.

**Solution :**

First let us draw a figure for the information given in the question.

Here AB represents height of the wall, BC represents the distance of the wall from the foot of the ladder.

In the right triangle ABC the side which is opposite to the angle 20 degree is known as opposite side (AB),the side which is opposite to 90 degree is called hypotenuse side (AC) and remaining side is called adjacent side (BC).

Now we need to find the length of the ladder (AC).

Cos θ = Adjacent side/Hypotenuse side

Cos θ = BC/AC

Cos 20° = 3/AC

0.9396 = 3/AC

AC = 3/0.9396

AC = 3.192

**Hence, the The length of the ladder is 3.192 m**. trigono

Let us look at the next problem on "Trigonometry word problems with solutions"

**Problem 7 : **

A kite flying at a height of 65 m is attached to a string inclined at 31° to the horizontal. What is the length of string ?

**Solution :**

First let us draw a figure for the information given in the question.

Here AB represents height of the kite. In the right triangle ABC the side which is opposite to angle 31 degree is known as opposite side (AB), the side which is opposite to 90 degree is called hypotenuse side (AC) and the remaining side is called adjacent side (BC).

Now we need to find the length of the string AC.

Sin θ = Opposite side/Hypotenuse side

Sin θ = AB/AC

Sin 31° = AB/AC

0.5150 = 65/AC

AC = 65/0.5150

AC = 126.2 m

**Hence, the length of the string is 126.2 m **

**Let us look at the next problem on "Trigonometry word problems with solutions"**

**Problem 8 :**** **

The length of a string between a kite and a point on the ground is 90 m. If the string is making an angle θ with the level ground such that tan θ = 15/8, how high will the kite be ?

**Solution :**

First let us draw a figure for the information given in the question.

Here AB represents height of the balloon from the ground. In the right triangle ABC the side which is opposite to angle θ is known as opposite side (AB), the side which is opposite to 90 degree is called hypotenuse side (AC) and remaining side is called adjacent side (BC).

Now we need to find the length of the side AB.

Tan θ = 15/8 --------> Cot θ = 8/15

Csc θ = √(1+ cot²θ)

Csc θ = √(1 + 64/225)

Csc θ = √(225 + 64)/225

Csc θ = √289/225

Csc θ = 17/15 -------> Sin θ = 15/17

But, sin θ = Opposite side/Hypotenuse side = AB/AC

AB/AC = 15/17

AB/90 = 15/17

AB = (15 x 90)/17

AB = 79.41

**Hence, the height of the tower is 79.41 m Hence**

**Let us look at the next problem on "Trigonometry word problems with solutions"**

**Problem 9 :**** **

An aeroplane is observed to be approaching the airpoint. It is at a distance of 12 km from the point of observation and makes an angle of elevation of 50 degree. Find the height above the ground.

**Solution :**

First let us draw a figure for the information given in the question.

Here AB represents height of the airplane from the ground.In the right triangle ABC the side which is opposite to angle 50 degree is known as opposite side (AB), the side which is opposite to 90 degree is called hypotenuse side (AC) and remaining side is called adjacent side (BC).

Now we need to find the length of the side AB.

From the figure given above, AB stands for the height of the aeroplane above the ground.

Sin θ = Opposite side/Hypotenuse side

Sin 50° = AB/AC

0.7660 = h/12

0.7660 x 12 = h

h = 9.192 km

**Hence, the height of the aeroplane above the ground is 9.192 km**

**Let us look at the next problem on "Trigonometry word problems with solutions"**

**Problem 10 :**** **

A balloon is connected to a meteorological station by a cable of length 200 m inclined at 60 degree angle . Find the height of the balloon from the ground. (Imagine that there is no slack in the cable)

**Solution :**

First let us draw a figure for the information given in the question.

Here AB represents height of the balloon from the ground. In the right triangle ABC the side which is opposite to angle 60 degree is known as opposite side (AB), the side which is opposite to 90 degree is called hypotenuse (AC) and the remaining side is called as adjacent side (BC).

Now we need to find the length of the side AB.

From the figure given above, AB stands for the height of the balloon above the ground.

Sin θ = Opposite side/Hypotenuse side

Sin θ = AB/AC

Sin 60° = AB/200

√3/2 = AB/200

AB = (√3/2) x 200

AB = 100√3

Approximate value of √3 is 1.732

AB = 100 (1.732)

AB = 173.2 m

**Hence, the height of the balloon from the ground is 173.2 m**

After having gone through the stuff given above, we hope that the students would have understood "Trigonometry word problems with solutions".

Apart from the stuff given above, if you want to know more about "Trigonometry word problems with solutions", please click here.

If you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**