Question

an observer, 1.5 m tall, is 28.5 m away from a tower 30 m high. find the angle of elevation of the top of the tower from his eye.

Answer 1

$\tan(\theta) =\dfrac{\text{opposite}}{\text{adjacent}}$

Find the angle of elevation:

$\tan(\theta) =\dfrac{\text{30 - 1.5}}{\text{28.5}}$

$\tan(\theta) =\dfrac{\text{28.5}}{\text{28.5}}$

$\tan(\theta) = 1$

$\theta = tan^{-1}(1)$

$\theta = 45 \textdegree$

Answer: The angle of elevation is 45°

Answer 2

Solution :

base=28.5 metres

tower height=30 metres

height of the man=1.5 metres

now...height of the tower with respect to the eye level of the man =(30-1.5)m=28.5 metres

now ...if theta be the angle of elevation

then ....

tan(theta)=height/base=(28.5/28.5)

tan(theta)=1

theta = \tan {}^{ - 1} (1) = 45°theta=tan

−1

(1)=45°

so the angle of elevation is 45°