The measure of side P to the nearest degree is 79 degrees.
Given:
ΔOPQ ,
O = 700 cm,
P = 840cm
Q = 620cm.
To find:
The measure of angle P.
According to the Law of Cosines:
In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. The law of cosines states:
[tex]cos A = b^{2} +c^{2} - a^{2} / 2bc[/tex]
Using Law of Cosines ΔOPQ, we get,
cos P = o² +q²- p² / 2oq
⇒ cos P = (700)² + (620)² -(840)² /2×700×620
⇒ Cos P = 490000 + 384400 - 705600 / 868000
⇒ Cos P = 168800/868000
on further simplification, we get,
Cos P = 0.19447
P = Cos⁻¹ (0.19447)
P = 78.786236
P = 79.
∴ the measure of angle P is 79 degrees.
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Therefore, the measure of angle P is 79 degrees.
