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djyliett [7]
3 years ago
7

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.

Mathematics
1 answer:
lina2011 [118]3 years ago
8 0

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 <em>OP</em> and Base is side <em>PN</em>.

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

\Rightarrow OP = PN \times tan59^\circ

Putting the values of <em>PN </em>and tan59^\circ.

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

Hence, the value of <em>OP </em>is 12.3\ feet.

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