In this section, you will learn how to solve angle of elevation trigonometry problems.

**Question 4 :**

To find the cloud ceiling, one night an observer directed a spotlight
vertically at the clouds. Using a theodolite placed 100 m from the
spotlight and 1.5 m above the ground, he found the angle of elevation to
be 60°. How high was the cloud ceiling? (Hint : See

figure)

cloud is present. The cloud ceiling at airports must be sufficiently high for safe take offs and landings. At night the cloud ceiling can be determined by illuminating the base of the clouds by a spotlight pointing vertically upward.)

**Solution :**

The side which is opposite to 90 degree is known as hypotenuse side, the side which is opposite to θ is known as opposite side and the remaining side is known as adjacent side.

In the given problem,we have to find the length of opposite side.

AC = Hypotenuse side

AB = Opposite side

BC = Adjacent side

tan θ = opposite side/adjacent side

tan 60° = AB/BC

**√**3 = AB/100

100 √3 = AB

AB = 100 **√**3

= 100 (1.732) = 173.2

Height of ceiling from ground = 173.2 + 1.5 = 174.7 m

**Question 5 :**

A simple pendulum of length 40 cm subtends 60° at the vertex in one full oscillation. What will be the shortest distance between the initial position and the final position of the bob? (between the extreme ends)

**Solution :**

In triangle OBC angle BOC = 30°

BC - opposite side

OC - hypotenuse side = 40 cm

AB - adjacent side

length of pendulum = 40 cm

sin θ = opposite side/hypotenuse side

sin 30° = BC/OC

1/2 = BC/40

40 = 2 BC

BC = 20 cm

length of AC = 2(BC) = 2(20) = 40 cm

**Question 6 : **

Two crows A and B are sitting at a height of 15 m and 10 m in two different trees vertically opposite to each other. They view a bread (an eatable) on the ground at an angle of depression 45° and 60° respectively. They start at the same time and fly at the same speed along the shortest path to pick up the bread. Which bird will succeed in it?

**Solution :**

In the given problem,we have to the length of AE and BE.

In triangle BED

BE - hypotenuse side

BD - opposite side

sin θ = Opposite side/Hypotenuse side

sin 60° = BD/BE

√3/2 = 10/BE

BE√3 = 10 x 2

BE = 20/√3 = 11.55 m

In triangle AEC,

AC - opposite side = 15 m

AE - hypotenuse side

sin θ = Opposite side/Hypotenuse side

sin 45° = AC/AE

1/√2 = 15/AE

AE = 15√2

= 21.21 m

The distance of BD is shorter than AE. So, bird "B" is having chance to succeed.

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

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**