When to use the law of cosine is explained below.
Using the labelled triangle, we have: sin D/d = sin E/e = sin F/f.
Using the sine law, the measure of angle M is: 74.9°.
What is the Cosine Law?
The cosine law is given as, c = a² + b² - 2ab(cos C). It is used to solve a triangle with missing angle or side.
What are the Two Instances When the Cosine Law is Applied?
When we are given two sides and an angle between the two sides, and we need to find the third side.
When we are given the all three sides of a triangle and we need to find the angles of the triangle.
What is the Law of Sines?
Using the labelled triangle DEF in the diagram below, the law of sines is:
sin D/d = sin E/e = sin F/f.
How to Find Angle M using the Law of Sines?
m∠N = 56°
n = 8.5 cm
m = 9.9 cm
Plug in the values into sin N/n = sin M/m:
sin 56/8.5 = sin M/9.9
sin M = (sin 56 × 9.9)/8.5
sin M = 0.9656
M = sin^(-1)(0.9656)
M = 74.9°
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