Question

Two cars are traveling towards a hotel on the same road. From the edge of the hotel, 600 feet high, Spiderman sits on the rooftop thinking about the depression angle needed to reach each car. If the depression angle to the nearest car is 52 degrees, and the depression angle to the farther car is 46 degrees, how far apart must the two cars be from each other?

Answer 1

Answer:

The distance between two cars is 110.64 feet.

Step-by-step explanation:

Angle of depression is defined as an angle between the line of sight and the horizontal.

Remember in a right angled triangle, the angle of depression is always same as the angle of elevation.

If $\theta$ be the angle of depression then,

$tan\theta=\frac{opposite}{adjacent}$

Given that,

Two car are travelling toward a hotel on the same road.

The height of the given building is 600 feet.

For the first car:

The angle of depression = The angle of elevation = 52°

Let the horizontal distance between the building and the car be x.

Here, $\theta =52 ^\circ$, opposite = 600 feet, adjacent = x

$tan 52^\circ=\frac{600}{x}$

$\Rightarrow x=\frac{600}{tan 52^\circ}$

$\Rightarrow x\approx 468.77$ feet

For the second car:

The angle of depression = The angle of elevation = 46°

Let the horizontal distance between the building and the car be y.

Here, $\theta =46 ^\circ$, opposite = 600 feet, adjacent = y

$tan 46^\circ=\frac{600}{y}$

$\Rightarrow y=\frac{600}{tan 46^\circ}$

$\Rightarrow x\approx 579.41$ feet

The distance between two cars is

= The distance of the second car from the building - The distance of the first car from the building

=(579.41-468.77) feet

=110.64 feet.