Make the given changes in the indicated examples of this section and then find the indicated values.

In Example 4, change 56.82 to 65.82 and then solve the triangle.

Data from Example 4

Solve the right triangle with b = 56.82 and c = 79.55.

We sketch the right triangle as shown in Fig. 4.35. Because two sides are given, we will use the Pythagorean theorem to find the third side a. Also, we will use the cosine to find ∠A. Because c² = a² + b² , a² = c² − b². Therefore,

To find ∠B, we use the fact that A + B = 90°, which means that we have B = 90° − A = 90° − 44.42° = 45.58°.
We have now found that a = 55.67 A = 44.42° B = 45.58°

Checking the sides and angles, we first note that side a is the shortest side and is opposite the smallest angle, ∠A. Also, the hypotenuse is the longest side. Next, using the sine function (we could use the cosine or tangent) to check the sides, we have

a = cb = 79.552 56.82 - 55.67 Because cos A = side adjacent A, we have hypotenuse 56.82 79.55 A = cos-1 cos A = 56.82 79.55/ = 44.42