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Paraphin [41]
2 years ago
13

In ΔNOP, n = 910 inches, o = 110 inches and p=820 inches. Find the measure of ∠P to the nearest degree.

Mathematics
2 answers:
Sophie [7]2 years ago
8 0

Given:

In ΔNOP, n = 910 inches, o = 110 inches and p=820 inches.

To find:

The measure of ∠P to the nearest degree.

Solution:

According to the law of cosine:

\cos A=\dfrac{b^2+c^2-a^2}{2bc}

Using law of cosine in triangle NOP, we get

\cos P=\dfrac{n^2+o^2-p^2}{2no}

Putting the given values, we get

\cos P=\dfrac{(910)^2+(110)^2-(820)^2}{2(910)(110)}

\cos P=\dfrac{828100+12100-672400}{200200}

\cos P=\dfrac{167800}{200200}

\cos P=0.83816

Taking cos inverse on both sides, we get

P=\cos^{-1}(0.83816)

P=(33.05367)^\circ

P\approx 33^\circ

Therefore, the measure of ∠P is 33°.

gladu [14]2 years ago
5 0

33° is the answer.

kinda in a hurry, but this is the answer to Deltamath

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