**Questions Based on Angle of Elevation :**

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

In order to solve word problems, first draw the picture to represent the given situation.

To find the questions 1 and 2, please visit the page "Angle of Elevation Practice Problems".

**Question 3 :**

To a man standing outside his house, the angles of elevation of the top and bottom of a window are 60° and 45° respectively. If the height of the man is 180 cm and if he is 5 m away from the wall, what is the height of the window? (√3 = 1.732)

**Solution :**

Height of window = AB

180 cm = 1.8 m

In triangle FBC,

tan θ = Opposite side / Adjacent side

tan 45 = BC/FC

1 = BC/5

BC = 5 m

In triangle FBC,

tan 60 = AC/FC

√3 = AC/5

AC = 5√3

AB = AC - BC

= 5√3 - 5

= 5(√3 - 1)

= 5(1.732 - 1)

= 5(0.732)

= 3.66 m

Hence height of window is 3.66 m.

**Question 4 :**

A statue 1.6 m tall stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 40° . Find the height of the pedestal. (tan 40° = 0.8391, √3 = 1.732)

**Solution :**

In triangle ABC,

tan θ = Opposite side / Adjacent side

tan 40 = BC/AB

0.8391 = BC/AB

Let BC = x

0.8391 = x/AB

AB = x/0.8391 -----(1)

In triangle ABD,

tan 60 = BD/AB

√3 = (1.6 + x)/AB

AB = (1.6 + x)/√3 -----(2)

(1) = (2)

x/0.8391 = (1.6 + x)/√3

√3x = (1.6 + x) 0.8391

1.732x - 0.8391x = 1.6(0.8391)

0.8929x = 1.34256

x = 1.34256/0.8929

x = 134256/89290

Hence the height of the pedestal is 1.5 m.

**Question 5 :**

A flag pole ‘h’ meters is on the top of the hemispherical dome of radius ‘r’ meters. A man is standing 7 m away from the dome. Seeing the top of the pole at an angle 45° and moving 5 m away from the dome and seeing the bottom of the pole at an angle 30° . Find (i) the height of the pole (ii) radius of the dome. (√3 = 1.732)

**Solution :**

In triangle ADB,

tan θ = Opposite side / Adjacent side

tan 45 = (r + h)/AB

1 = (r + h)/(r + 7)

r + h = r + 7

r - r + h = 7

h = 7 m

In triangle ADC,

tan 30 = AE/AC

1/√3 = r / (r + 12)

r + 12 = √3r

r(1 - √3) = -12

r = [12/(√3 - 1)] [(√3 + 1)/(√3 + 1)]

= 12(√3 + 1)/2

= 6(1.732 + 1)

= 6(2.732)

r = 16.39 m

(i) the height of the pole = 7m

(ii) radius of the dome = 16.39 m

After having gone through the stuff given above, we hope that the students would have understood, "Questions Based on Angle of Elevation".

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