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3 years ago

15

In triangle ABC, the length of side AB is 16 inches and the length of side BC is 23 inches. Which of the following could be the

length of side AC?
a 31 inches
b44 inches
c5 inches
d41 inches

1 answer:

Aleksandr [31]3 years ago

4 0

A 31 inches is the answer because it can't be higher than 39

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Triangle ABC has side lengths a= 24, b= 40, and c= 55. What is the measure of angle C? 83.6° 116.2° 23.0° 40.7°

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<h3>Answer: 116.2°</h3>

Work Shown:

$c^2 = a^2 + b^2 - 2ab\cos(C)\\\\55^2 = 24^2 + 40^2 - 2*24*40\cos(C)\\\\3025 = 576 + 1600 - 1920\cos(C)\\\\3025 = 2176 - 1920\cos(C)\\\\3025 - 2176 = -1920\cos(C)\\\\849 = -1920\cos(C)\\\\-1920\cos(C) = 849\\\\\cos(C) = (849)/(-1920)\\\\\cos(C) \approx -0.4421875\\\\C \approx \cos^{-1}(-0.4421875)\\\\C \approx 116.243535748231^{\circ}\\\\C \approx 116.2^{\circ}\\\\$

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