Based on the information, the measure of ∠P is approximately 76.4 degrees.
How to solve the triangleApplying the Law of Cosines to ∠P, we have:
p² = o² + q² - 2oq * cos(∠P)
Substituting the given values:
89² = 30² + 95² - 2 * 30 * 95 * cos(∠P)
7921 = 900 + 9025 - 5700 * cos(∠P)
Now, let's simplify the equation:
7921 = 9025 - 4800 * cos(∠P)
Rearranging the terms:
4800 * cos(∠P) = 9025 - 7921
4800 * cos(∠P) = 1104
cos(∠P) = 1104 / 4800
cos(∠P) = 0.23
Now, we need to find the inverse cosine (arccos) of 0.23 to determine the measure of ∠P.
∠P = arccos(0.23)
∠P ≈ 76.4 degrees
Therefore, the measure of ∠P is approximately 76.4 degrees.
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