Question

In ΔNOP, the measure of ∠P=90°, the measure of ∠N=59°, and PN = 7.4 feet. Find the length of OP to the nearest tenth of a foot.

Answer 1

12.3 feet.

Explanation:

As we are given that
`\triangle NOP` is an right angled triangle.

`\angle P = 90 ^\circ \\\angle N = 59 ^\circ\\Side\ PN = 7.4 \text{ feet}`

And we have to find out the value of side OP to the nearest tenth of a foot by rounding off the value as seen in the attached figure as well.

By using Trigonometric functions in a right angled
`\triangle`, we know that:

`tan \theta = (Perpendicular)/(Base)`

Here,
`\theta` is
`\angle N`, Perpendicular is side OP and Base is side PN.

So,
`tan 59^\circ = (OP)/(PN)`

`\Rightarrow OP = PN * tan59^\circ`

Putting the values of PN and
`tan59^\circ`.

`OP = 1.66 * 7.4\\\Rightarrow OP = 12.3 ft`

Hence, the value of OP is
`12.3\ feet`.