Answer:
Measure of angle A = 61.9°
Explanation:
- Because we want to find an angle measure and the triangle is a right triangle (i.e., a triangle with a right angle), we can find the measure of angle A using inverse trigonometry.
When angle A is the reference angle, we see that:
- AB is the adjacent side,
- BC is the opposite side,
- and AC is the hypotenuse (i.e., the side opposite the right angle).
Thus, we can find the measure of angle A using the cosine ratio, whose general equation is given by:
cos^-1 (adjacent / hypotenuse) = θ, where
- θ is the reference angle.
Since AB (the side adjacent to angle A) is 8 units and AC (the hypotenuse) is 17 units, we can plug in 8 for the adjacent side and 17 for the hypotenuse to find θ, the measure of angle A:
cos^-1 (8/17) = θ
61.92751306 = θ
61.9 = θ
Thus, the measure of angle A is about 61.9°.