You are standing on top of a building looking down at your friend who is getting chased by a zombie. The building is 150 feet tall. When your friend looks up, the angle of elevation is 50°. When the zombie looks up at you, the angle of elevation is 25°.

a) 125.865 ft

b) 321.676 ft

c) 195.811 ft

Step-by-step explanation:

Given:-

- The height of the building, H = 150 ft

- The angle of elevation (friend - top of building), θ1 = 50°

- The angle of elevation (zombie - top of building), θ2 = 25°

Find:-

a) How far away is your friend from the building

b) How far away is the zombie from the building

c) How far away is the zombie from your friend

Solution:-

- We will consider the two right angle triangles with similar height (H) which denotes the height of the building.

- The distance your friend is from the building is (x1) and looks up to the top of the building with angle of elevation of (θ1).

- We can apply the trigonometric ratio for the right angle triangle formed between your friend, foot of the building and you (on top of the building):

tan (θ1) = H / x1

x1 = H / tan (θ1)

x1 = 150 / tan (50°)

x1 = 125.865 ft ... Answer (a)

- The distance zombie is from the building is (x2) and looks up to the top of the building with angle of elevation of (θ2).

- Similarly, apply the appropriate trigonometric ratio for the right angle triangle formed between zombie, foot of the building and you (on top of the building):

tan (θ2) = H / x2

x2 = H / tan (θ2)

x2 = 150 / tan (25°)

x2 = 321.676 ft ... Answer (b)

- The distance between your friend and the zombie (s) can now be determined from subtracting the distance of your friend from the building from distance of the zombie from the building:

s = x2 - x1

s = 321.676 - 125.865

s = 195.811 ft ... Answer (c)