Question

A plane is 3 miles above the ground, 15 miles from its destination. What is the angle of elevation of the plane from its destination?

Answer 1

angle of elevation = 11.3°

Explanation:

To solve this problem, it helps to draw a diagram of the scenario.

From the diagram below, we can see that the angle of elevation is marked Θ. This is the angle formed between the ground and the line of elevation of the plane from the destination.

We can also see that a right-angled triangle is formed when all the distances are labelled.

To find the angle of elevation of the plane from its destination, we have to solve for Θ. We can see that the side opposite the angle Θ is labelled 3 miles (height of plane above ground). The side adjacent to Θ is labelled 15 miles (distance of plane from destination). The trigonometric ratio that relates opposite and adjacent is tan. Therefore:

`\mathrm{tan\ \theta = (opposite)/(adjacent)}`

⇒
`\mathrm{tan \ \theta =} (3)/(15)`

⇒
`\theta = \mathrm{tan}^(-1)((3)/(15))`

⇒
`\theta = 11.3^(\circ)`

Therefore, the angle of elevation of the plane from its destination is 11.3°.