Question

An airplane pilot over the Pacific sights an atoll at the angle of depressionof 5º. At this time, the horizontal distance from the airplane to the atoll is4,535 meters. What is the height of the plane to the nearest meter?

Answer 1

397 meters

Step-by-step explanation:

Let us draw a diagram to understand the situation better.

Where H is the height of the plane.

Now the tan ratio for 5° gives

`\tan 5^o=\frac{opposite}{\text{adjacent}}`

Since opposite = H and adjacent = 4535 meters, the above gives

`\tan (5^o)=(H)/(4535)`

Multiplying both sides by 4535 gives

`\tan (5^o)*4535=H`

Since tan(5°) =0.0875.., ( just used a calculator to find out) the above becomes

`0.0875*4535=H`
`H=396.8125`

rounding to the nearest meter gives

`\boxed{H=397.}`