Question

A boy observes the tip of a tower fixed on the top of a building of
height 14m from a point on the ground, then the angle of elevation
is 45 degree. While walking towards the building again he observes the
tip and base of the tower from another point, now if angles of
elevation are 60degree and 30degree respectively. Find the height of the tower
and the distance he walked.​

Answer 1

Answer:

Ya it's very easy question for solving trignonetry

Answer 2

Recall:

$\tan \theta = \dfrac{\text{Opposite}}{\text{Adjacent}}$

Find the distance from the point after he has walked and the building:

$\text{Let the distance be x. (see attached image)}$

$\tan \theta = \dfrac{\text{Opposite}}{\text{Adjacent}}$

$\tan (30) =\dfrac{14}{x}$

$x =\dfrac{14}{\tan (30)}$

$x = 24.25 \text { m}$

Find the height of the tower:

$\text{Let H be the distance from the tip of the tower to the ground.}$

$\tan \theta = \dfrac{\text{Opposite}}{\text{Adjacent}}$

$\tan (60) = \dfrac{14 + H}{24.25}$

$14 + H = 24.25\tan(60)$

$H = 24.25\tan(60) - 14$

$H = 28 \text { m}$

$\text {Height of the tower} = 28 - 14$

$\text {Height of the tower} = 14 \text { m}$

Find the distance from the point before he has walked and the building:

$\text{Let the distance be y. (see attached image)}$

$\tan \theta = \dfrac{\text{Opposite}}{\text{Adjacent}}$

$\tan (45) =\dfrac{28}{y}$

$y =\dfrac{28}{\tan{45}}$

$y = 28 \text { m}$

Find the distance he has walked:

$\text{Distance walked = }28 - 24.25$

$\text{Distance walked = }3.75 \text { m}$

Answer: Height of the tower = 14 m. Distance walked = 3.75 m