4. Simon is standing on the street corner. Simon's eyes are 6 feet off of the ground. He is looking
down at a cockroach on a box that is one foot off of the ground. If he is looking downward at an
angle of 40°, how far is he from the cockroach?

He is 4.2 ft from the cockroach

Step-by-step explanation: Please refer to the attached diagram.

If Simon is staring at a cockroach with his eyes 6 ft from the ground, then Simon’s position would be depicted as point E. Then the cockroach is on a box which is 1 ft off from the ground. That means Simon is actually looking at the cockroach not exactly on the ground, but at a distance of 1 ft from the ground and that means Simon’s eyes are looking at the cockroach from a distance of 5 ft FROM THE GROUND. So the cockroach’s position is depicted by point C on the triangle. Hence the triangle in the diagram shows Simon (point E) looking down at an angle of 40, the cockroach at point C and the ground marked as point G.

Therefore the distance between Simon and the cockroach is marked by line GC (labeled as x in the diagram).

Using E as the reference angle, we have an adjacent (the line between the reference angle and the right angle) which is 5ft, and an opposite (facing the reference angle) which is x.

Using trigonometric ratios,

Tan E = opposite/adjacent

Tan 40 = x/5

0.8391 = x/5

By cross multiplication we now have

5 (0.8391) = x

4.1955 = x

Approximately 4.2

Hence Simon is 4.2 ft away from the cockroach