TRIGONOMETRY WORD PROBLEMS WITH 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.

Problems

Problem 1 :

From the top of a rock 503 m high, the angle of depression of a car on the ground is observed to be 30°. Find the distance of the car from the rock.

Solution :

BC = Rock,

Car in the position A.

tan θ  =  Opposite side / Adjacent side

tan 30  =  BC/AB

1/3  =  503/AB

AB  =  503(3)

AB  =  50(3)

AB  =  150 m

The distance of the car from the rock is 150 m.

Problem 2 :

The horizontal distance between two buildings is 70 m. The angle of depression of the top of the first building when seen from the top of the second building is 45°. If the height of the second building is 120 m, find the height of the first building.

Solution :

CE  =  120 m

Let DC = x

BC   =  DC  =  70 m

tan 45  =  DE/AD

1  =  (120 - x)/70

70  =  120 - x

x  =  120 - 70

x  =  50 m

So, the height of the 1st building is 50 m

Problem 3 :

From the top of the tower 60 m high the angles of depression of the top and bottom of a vertical lamp post are observed to be 38° and 60° respectively. Find the height of the lamp post. (tan 38° = 0.7813, 3 = 1.732)

Solution :

Height of tower  =  60 m

Let DC = x, ED  =  60 - x

tan 38  =  DE/AD

0.7813  =  (60 - x)/AD

AD  =  (60 - x)/ 0.7813 ---(1)

In triangle BEC,

tan 60  =  EC/BC

√3  =  60/BC

BC  =  60/√3

BC  =  20√3 ------(2)

(1)  =  (2)

(60 - x)/0.7813  =  20√3

60 - x  =  20(0.7813)(1.732)

60 - x  =  34.64(0.7813)

60 - x  =  27.06

x  =  60 - 27.06

x  =  32.94

So, the height of the vertical lamp post is 32.94 m

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

Word problems on quadratic 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