Question

A straight highway leads to the foot of the tower. A man standing on the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. After covering a distance of 50 m, the angle of depression of the car becomes 60°. Find the height the tower.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Recall the following for this question:

Adjacent angles on a straight line adds up to 180°

Sine Rule:

           $\dfrac{a}{\sin A} = \dfrac{b}{\sin B}$

Cosine Identity:

           $\cos \theta = \dfrac{\text{adjacent}}{\text{hypotenuse}}$

Find the angle ACD:

$\angle ACD = 180 - 60$

$\angle ACD = 120^\circ$

Find the angle CAD:

$\angle CAD = 180 - 120 - 30$

$\angle CAD = 30^\circ$

In △ACD, Find AD:

$\dfrac{AD}{\sin(120)} = \dfrac{50}{\sin(30)}$

$AD \sin (30) = 50 \sin(120)$

$AD = \dfrac{50 \sin(120)}{\sin (30) }$

$AD =50\sqrt{3} \text { m}$

Find the angle BAD:

$\angle BAD = 180 - 30$

$\angle BAD = 60^\circ$

In △ABD, Find AB:

$\cos \theta = \dfrac{AB}{AD}$

$\cos (60) = \dfrac{AB}{50\sqrt{3} }$

$AB= 50\sqrt{3} \times \cos (60)$

$AB= 25\sqrt{3} \text { m}$

Answer: The height of the tower is 25√3 m tall