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

Answer:

12.3 feet.

Step-by-step 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:

$tan \theta = \frac{Perpendicular}{Base}$

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

So, $tan 59^\circ = \frac{OP}{PN}$

$\Rightarrow OP = PN \times tan59^\circ$

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

$OP = 1.66 \times 7.4\\\Rightarrow OP = 12.3 ft$

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