Question

A man stands on a balcony 140 feet up and sees a bus stop at a 75 degree angle How far is the bus stop to the man in nearest feet

Answer 1

Answer:

145 feet  far is the bus stop to the man in nearest feet.

Step-by-step explanation:

Let the height of the balcony from the ground be h and the distance from the bus stop to the man be x.

As per the statement:

A man stands on a balcony 140 feet up and sees a bus stop at a 75 degree angle.

⇒ h = 140 feet and angle of depression= $75^{\circ}$

We know that:

Angle of elevation$(\theta)$ = Angle of depression = 75 degree

using the sine ratio we have;

$\sin 75^{\circ} = \frac{140}{x}$

⇒$x = \frac{140}{\sin 75^{\circ}}$

⇒$x = \frac{140}{0.96592582628}$

Simplify:

$x = 144.938665$ feet

Therefore, 145 feet  far is the bus stop to the man in nearest feet.

Answer 2

D = 140 sec Θ models the distance from the man 
to any object given his angle of sight theta. 
after working it out you will find out that the awnser is 541 feet