**Angle of Elevation and Depression Worksheet :**

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

To find questions 1 to 3, please visit the page "Problems involving angle of elevation and depression"

**Question 4 :**

The angle of elevation of the top of a cell phone tower from the foot of a high apartment is 60° and the angle of depression of the foot of the tower from the top of the apartment is 30° . If the height of the apartment is 50 m, find the height of the cell phone tower. According to radiations control norms, the minimum height of a cell phone tower should be 120 m. State if the height of the above mentioned cell phone tower meets the radiation norms.

**Solution :**

In triangle BEC,

tan θ = Opposite side / Adjacent side

tan 60 = EC/BC

√3 = (50 + x)/BC

BC = (50 + x)/√3 ----(1)

In triangle ABD,

tan 30 = AB / BC

1/√3 = 50/BC

BC = 50√3 ----(2)

(1) = (2)

(50 + x)/√3 = 50√3

50 + x = 50√3√3

50 + x = 150

x = 150 - 50

x = 100

Height of cell phone tower = 100 + 50

= 150 m

Hence the cell phone tower meets the radiation norms.

**Question 5 :**

The angles of elevation and depression of the top and bottom of a lamp post from the top of a 66 m high apartment are 60° and 30° respectively. Find (i) The height of the lamp post. (ii) The difference between height of the lamp post and the apartment. (iii) The distance between the lamp post and the apartment. (√3 = 1.732)

**Solution :**

In triangle AED,

tan 60 = ED/AD

√3 = ED/AD

AD = ED/√3 -----(1)

In triangle ABC,

tan 30 = AB/BC

1/√3 = 66/BC

BC = 66√3 -----(2)

(1) = (2)

ED/√3 = 66√3

ED = 66(3)

ED = 198

(i) Height of lamp post = ED + DC

= 198 + 66

= 264 m

(ii) The difference between height of the lamp post and the apartment

= 264 - 66

= 198 m

(iii) The distance between the lamp post and the apartment

BC = 66√3

= 66(1.732)

= 114.31 m

**Question 6 :**

Three villagers A, B and C can see each other across a valley. The horizontal distance between A and B is 8 km and the horizontal distance between B and C is 12 km. The angle of depression of B from A is 20° and the angle of elevation of C from B is 30° . Calculate : (i) the vertical height between A and B. (ii) the vertical height between B and C. (tan 20° = 0.3640, √3 = 1.732)]

**Solution : **

In the left side triangle,

tan 20 = Vertical distance of AB/8

0.3640 = Vertical distance of AB/8

Vertical distance of AB = 0.3640(8)

Vertical distance of AB = 2.91 km

In the right side triangle,

tan 30 = Vertical distance of BC/12

1/√3 = Vertical distance of BC/12

Vertical distance of BC = 12/√3

= 12(√3/3)

= 4√3

= 4(1.732)

= 6.928

Vertical distance of BC = 6.93 km

After having gone through the stuff given above, we hope that the students would have understood how to do problems on 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 the 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**