Question

A 6 foot shadow is cast by a 10 foot lamp post. What is the angle of elevation of the sun?

Answer 1

Let that be theta

• tanØ=Perpendicular/Base

Here perpendicular is lamp post and base is the shadow

• tanØ=10/6
• tanØ=5/3
• tanØ=1.67
• Ø=59°

Answer 2

59.0° (nearest tenth)

Explanation:

This can be modeled as a right triangle (see attachment).

To find the angle of elevation (marked as
`x` on the attached diagram), use the tan trig ratio:

Tan trigonometric ratio

`\sf\tan(\theta)=(O)/(A)`

where:

• 
  `\theta` is the angle
• O is the side opposite the angle
• A is the side adjacent the angle

Given:

• 
  `\theta = x`
• O = 10
• A = 6

Substitute the given values into the formula and solve for x:

`\implies \sf\tan(\theta)=(10)/(6)`

`\implies \sf\theta=\tan^(-1)\left((10)/(6)\right)`

`\implies \theta = \sf 59.03624...^(\circ)`

`\implies \theta = \sf 59.0^(\circ)\:(nearest\:tenth)`