To find the measure of angle A, we can use the law of cosines:
cos(A) = (b^2 + c^2 - a^2) / 2bc
In this case, side a is opposite angle A (side BC), side b is opposite angle B (side AC), and side c is opposite angle C (side AB).
Plugging in the values:
cos(A) = (8^2 + 15^2 - 17^2) / (2 * 8 * 15)
cos(A) = (64 + 225 - 289) / 240
cos(A) = 0.16667
Now, to find the measure of angle A, we use the inverse cosine function:
A = cos^(-1)(0.16667)
A ≈ 80 degrees
Therefore, the approximate measure of angle A is 80 degrees.
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 find the approximate interior angle measure at vertex A
. Round your answer to the nearest whole degree.
1 answer