In ΔOPQ, o = 30 cm, p = 89 cm and q=95 cm. Find the measure of ∠P

Answers

Answer 1

Based on the information, the measure of ∠P is approximately 76.4 degrees.

How to solve the triangle

Applying 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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