Question

In ΔABC, m∠B = 90°, cos(C) = , and AB = 16 units. Based on this information, m∠A =(62,33,28) °, m∠C =(62,33,28) °, and AC = (22,34,10) units. Note that the angle measures are rounded to the nearest degree.

Answer 1

Using the cosine of ∠C and the length of AB, we can calculate the length of AC in ΔABC and then determine m∠A and m∠C since the angles in a triangle sum to 180°, and the angles in a right triangle sum to 90°.

Step-by-step explanation:

Given ΔABC, where m∠B = 90° and cos(C), we can determine the measurements of the remaining angles and the length of side AC using trigonometric relationships. Since the cosine of an angle in a right triangle is the adjacent side over the hypotenuse, we can calculate AC by using the formula AC = AB * cos(C). Once we have the length of AC, we can find m∠A and m∠C through the properties of right triangles, knowing the sum of angles in a triangle is always 180°, and in a right triangle, the other two angles must sum to 90°.

For example, if we were given a specific cosine value for ∠C, we could calculate the exact values for m∠A, m∠C, and AC.