Question

A forest ranger stands at the top of a 120 foot fire tower. He spots a fire 900 feet away from the base of the tower. What is the angle of elevation from the fire to the top of the fire tower? Round your answer to the nearest tenth of a degree.

Answer 1

Answer:
`7.6\°`

Explanation:

You need to draw a right triangle as the one attached, where
`\alpha` is the angle of elevation from the fire to the top of the fire tower.

You need to use the Inverse trigonometric function Arctangent:

`\alpha= arctan((opposite)/(adjacent))`

Observe the triangle. You can identify that:

`opposite=120\\adjacent=900`

Then, you can substitute values:

`\alpha= arctan((120)/(900))`

Finally, evaluating, you get that the angle of elevation from the fire to the top of the fire tower is the following:

`\alpha =7.59\°`

Rounded to the the nearest tenth of a degree:

`\alpha\approx7.6\°`