The sides and angles of triangle upper A upper B and upper C are labeled. Side upper B upper A is labeled 45 and side upper C upper A is labeled 32. Angle upper C is marked with a small square box.
Use the inverse of cosine to find the interior angle measure of vertex A
. Round your answer to the nearest whole degree.
To find the interior angle measure of vertex A, we can use the Law of Cosines:
cos(angle C) = (a^2- b^2 - c^2) / (2bc)
Plugging in the values we know, we get:
cos(angle C) = (45^2 - 32^2 - 32^2) / (2 * 45 * 32)
cos(angle C) = (2025 - 1024 - 1024) / 2880
cos(angle C) = -23 / 2880
Now, we can take the inverse cosine of -23 / 2880 to find the measure of angle C:
angle C = cos^−1(-23 / 2880)
angle C ≈ 94.14 degrees
Since the sum of the interior angles in a triangle is 180 degrees, we can find the measure of angle A:
angle A = 180 - angle B - angle C
angle A = 180 - 45 - 94.14
angle A ≈ 40.86 degrees
Therefore, the interior angle measure of vertex A is approximately 41 degrees.