**Trigonometry Problems Involving Angle of Depression :**

Here we are going to see, some example problems based on angle of depression.

**Angle of Depression :**

The angle of depression is an angle formed by the line of sight with the horizontal when the point is below the horizontal level. That is, the case when we lower our head to look at the point being viewed.

To find questions 1 to 3, please visit the page "Trigonometry Word Problems with Angle of Depression"

**Question 4 :**

An aeroplane at an altitude of 1800 m finds that two boats are sailing towards it in the same direction. The angles of depression of the boats as observed from the aeroplane are 60° and 30° respectively. Find the distance between the two boats. (√3 = 1.732)

**Solution :**

In triangle ABC,

tan θ = Opposite side / Adjacent side

tan 60 = AB/BC

√3 = 1800/BC

BC = 1800/√3

BC = 600√3

In triangle ABD,

tan 30 = AB / BD

1/√3 = 1800/ BD

BD = 1800√3

Distance between two boats = CD

= BD - BC

= 1800√3 - 600√3

= 1200 √3

= 1200(1.732)

Distance between two boats = 2078.4 m

**Question 5 :**

From the top of a lighthouse, the angle of depression of two ships on the opposite sides of it are observed to be 30° and 60°. If the height of the lighthouse is h meters and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is 4h/√3 m.

**Solution :**

In triangle ADC,

tan 30 = DC/AC

1/√3 = h/AC

AC = √3 h -----(1)

In triangle DCB,

tan 60 = DC/BC

√3 = h/BC

BC = h/√3 -----(2)

(1) + (2)

AC + BC = √3 h + (h/√3)

Distance between two ships = (3h + h)/√3

Distance between two ships = 4h/√3

Hence proved.

**Question 6 :**

A lift in a building of height 90 feet with transparent glass walls is descending from the top of the building. At the top of the building, the angle of depression to a fountain in the garden is 60°. Two minutes later, the angle of depression reduces to 30°. If the fountain is 30√3 feet from the entrance of the lift, find the speed of the lift which is descending.

**Solution :**

Let "x" be the speed of the lift

In triangle ABD,

After having gone through the stuff given above, we hope that the students would have understood how to solve trigonometry problems on angle of elevation.

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

Widget 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**