The sides and angles of triangle upper A upper B and upper C are labeled. Side upper A upper B is labeled 17, side upper A upper C is labeled 8, and side upper C upper B is labeled 15. Angle upper C is marked with a small square box.
Use the inverse of cosine to calculate the approximate interior angle measure at vertex B
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(1 point)
Responses
90°
90°
28°
28°
34°
34°
62°
To find the interior angle measure at vertex B, we first need to calculate the angle at vertex C using the Law of Cosines:
Cos(C) = (a^2 + b^2 - c^2) / 2ab
where a = 17, b = 8, and c = 15.
Cos(C) = (17^2 + 8^2 - 15^2) / (2*17*8)
Cos(C) = (289 + 64 - 225) / 272
Cos(C) = 128 / 272
Cos(C) = 0.47
Therefore, angle C is approximately 62 degrees.
Since the sum of interior angles in a triangle is 180 degrees, we can now find the angle at vertex B:
Angle B = 180 - angle A - angle C
Angle B = 180 - 90 - 62
Angle B = 28
Therefore, the approximate interior angle measure at vertex B is 28 degrees. The answer is:
28°