# ANGLE OF ELEVATION AND DEPRESSION QUESTIONS

Angle of Elevation and Depression Questions :

Here we are going to see some practice questions on angle of elevation and depression word problems.

## Angle of Elevation and Depression Questions - Practice questions

Question 15 :

The angles of elevation of an artificial earth satellite is measured from two earth stations, situated on the same side of the satellite, are found to be 30° and 60°. The two earth stations and the satellite are in the same vertical plane. If the distance between the earth stations is 4000 km, find the distance between the satellite and earth. (3 = 1.732)

Solution : BC = x m

In triangle ABC :

∠ACB  =  60°

tan θ = opposite side/Adjacent side

tan 60°  =  AB/BC

√3  =  AB/BC

AB = √3BC

AB = x√3 ----(1)

In triangle ABD :

tan θ = opposite side/Adjacent side

tan 30°  =  AB/BD

1/√3  =  AB/(BC + CD)

1/√3  =  AB/(x + 4000)

AB = (x + 4000)/√3 ---->(2)

(1) = (2)

x√3  =  (x + 4000)/√3

3 x =  x + 4000

3x - x = 4000

2x = 4000

x = 2000

distance between the satellite and earth(AB) = x√3

=  2000 (1.732)  =  3464 km

Question 16 :

From the top of a tower of height 60 m, the angles of depression of the top and the bottom of a building are observed to be 30° and 60° respectively. Find the height of the building.

Solution :

From the given information, we can draw a rough diagram In triangle ABC :

Let AB = x  and BD = 60 - x

∠ACB  =  30°

tan θ = opposite side/Adjacent side

tan 30°  =  AB/BC

1/√3  =  x/BC

BC = x √3 ----(1)

∠AED  =  60°

tan θ = opposite side/Adjacent side

√3  =  60/DE

DE = 60/√3 ----(2)

(1)  =  (2)

√3  =  60/√3

3x = 60

x = 20 m

CE = 60 - 20 = 40 m

Height of the building = 40 m. After having gone through the stuff given above, we hope that the students would have understood "Angle of Elevation and Depression Questions".

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

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

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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 