Answer:
LAW OF COSINES
==============================
\large \bold{\blue{Question:}}Question: What is the measure of the smallest angle in ∆ABC with sides a = 7, b = 16 and c = 10 ?
A. 16.39°
B. 25.36°
C. 32.25°
D. 57.75°
\large \bold{\blue{Answer:}} \: \: \LARGE \tt \green{A. \ 16.39 \sf °}Answer:A. 16.39°
\large \bold{\blue{Reason:}}Reason: Since the triangle gives three sides (SSS), we will be using the law of cosines.
» Remember that the opposite angle of the shortest side of a triangle was the smallest angle. In this case, since side (a) was the shortest side, we'll gonna find the measure of angle A.
\sf cos \: A = \frac{b² \ + \ c² \ - \ a²}{2bc}cosA=
2bc
b² + c² − a²
\sf cos \: A = \frac{16² \ + \ 10² \ - \ 7²}{2(16)(10)}cosA=
2(16)(10)
16² + 10² − 7²
\sf cos \: A = \frac{256 \ + \ 100 \ - \ 49}{2(16)(10)}cosA=
2(16)(10)
256 + 100 − 49
\sf cos \: A = \frac{307}{320}cosA=
320
307
\sf \angle A = cos^{-1}(\frac{307}{320})∠A=cos
−1
(
320
307
)
\sf \angle A = 16.39°∠A=16.39°
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