Question

Ranger Chris spots a fire at an angle of depression of 20° from his 70 feet tall tower. How far is the fire from the base of the tower?

A) 23.94 ft
B) 25.48 ft
C) 192.32 ft
D) 204.67 ft

Answer 1

To find the distance between Ranger Chris and the fire, we can use trigonometry. The fire is approximately 192.32 ft away from the base of the tower.

Step-by-step explanation:

To find the distance between Ranger Chris and the fire, we can use trigonometry. Let's consider the right triangle formed by the height of the tower, the distance from the base of the tower to the fire, and the angle of depression. The tangent function relates the opposite side (height of the tower) and the adjacent side (distance from the base of the tower to the fire).

Tan(angle of depression) = opposite/adjacent.

Tan(20°) = 70/adjacent.

To find the adjacent side, we can rearrange the equation:

Adjacent = opposite / tan(angle of depression).

Using the values given, we have:

Adjacent = 70 / tan(20°) ≈ 192.32 ft.

Therefore, the fire is approximately 192.32 ft away from the base of the tower.