Question

A detective knows what time of day it is based on the angle at which the sun is hitting a man. Suppose a detective is looking at a photograph of a 6-foot tall man with a shadow that is 3.5 feet. Find the angle at which the sun is hitting the ground.

Answer 1

The angle
`\theta` at which the sun is hitting the ground is:

`\theta\approx 59.74^o`

Explanation:

You can use right angle trigonometry to solve this, since the man (6 ft tall) and the shadow on the ground (3.5 ft long) form a right angle triangle as shown on the attached image.

The use the tangent function to find the angle that the sun's rays make with the ground:

`tan(\theta)=(opposite)/(adjacent) \\tan(\theta)=(6)/(3.5) \\\theta=arctan((6)/(3.5))\\\theta\approx 59.74^o`