**Example Problems of Angle of Elevation and Depression :**

Here we are going to see some example problem of trigonometry using angle of elevation and depression.

**Question 13 :**

A boy standing on the ground, spots a balloon moving with the wind in a horizontal line at a constant height . The angle of elevation of the balloon from the boy at an instant is 60°. After 2 minutes, from the same point of observation,the angle of elevation reduces to 30°. If the speed of wind is 29√3 m/min. then, find the height of the balloon from the ground level.

**Solution :**

Distance covered by the balloon = BC

BC = Time x Speed ==> 2 x 29 √3 ==> 58√3 m

AB = x then AC = x + 58√3

In triangle DAC :

∠DAC = 30°

tan θ = opposite side/Adjacent side

tan 30° = DC/AC

1/√3 = DC/(x + 58√3)

DC = (x + 58√3)/√3 ----(1)

In triangle EAB :

∠EAB = 60°

tan θ = opposite side/Adjacent side

tan 60° = EB/AB

√3 = EB/x

x√3 = EB

EB = √3x ---->(2)

Since EB = DC

(1) = (2)

(x + 58√3)/√3 = √3x

x + 58√3 = 3x

3x - x = 58√3

2x = 58√3

x = 58√3/2 ==> 29√3 m

Height of the balloon from ground level EB = √3 x

= 29 √3 (√3)

= 29(3) ==> 87 m

Hence height of the balloon from ground level = 87 m.

**Question 14 :**

A straight highway leads to the foot of a tower . A man standing on the top of the tower spots a van at an angle of depression of 30°. The van is approaching the tower with a uniform speed. After 6 minutes, the angle of depression of the van is found to be 60°. How many more minutes will it take for the van to reach the tower?

**Solution :**

From the given information, we can draw a rough diagram

Distance covered by the van to reach D from C = 6 minutes

time taken = x

Distance between D and C = 6x

In triangle ACB

∠ACB = 30°

tan θ = opposite side/Adjacent side

tan 30° = AB/BC

1/√3 = AB/(BD+DC)

1/√3 = AB/(BD+6x)

(BD+6x)/√3 = AB ----(1)

In triangle ABD

∠ABD = 60°

tan θ = opposite side/Adjacent side

tan 60° = AB/BD

√3 = AB/BD ==> AB = BD√3 -----(2)

(1) = (2)

(BD+6x)/√3 = BD√3

BD + 6x = BD(3)

3BD - BD = 6x

2BD = 6x

BD = 6x /2 = 3x

Here 3 represents number of minutes covered by the van and x stands for time taken.

Hence 3 more minutes will it take for the van to reach the tower.

After having gone through the stuff given above, we hope that the students would have understood "Example Problems of Angle of Elevation and Depression".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**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**

**Trigonometry 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**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**