Trig law of cosines

determine the approximate measure of angle c.

90.0 degrees

95.7 degrees

60.9 degrees

102.3 degrees

C ≈ 95.7°

Step-by-step explanation:

Law of cosines:

c² = a² + b² − 2ab cos C

where a, b, and c are the sides of the triangle, and C is the angle opposite of side c.

9² = 5² + 7² − 2(5)(7) cos C

81 = 25 + 49 − 70 cos C

81 = 25 + 49 − 70 cos C

7 = -70 cos C

-1/10 = cos C

C ≈ 95.7°

answer rather than having to add and subtract the measurements of the semi-circle, notice that the semicircle to the left of ad is actually identical in area to the blank semicircle-shaped space to the left of bc. so if we transferred the red semicircle into the blank space, we would end up with a square of side length 24 cm. the area of a square is s^2 = 24^2 = 676 cm^2.

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