Exercise 23 Page 924

First, let's draw the measurements from the exercise on a right triangle to visualize the given information.

We will find the missing measures one at a time. In this case, this means that we want to find m ∠ A, m ∠ B, and a.

Angle Measures

We can find m ∠ A using a cosine ratio.

The cosine of ∠ A is the ratio of the length of the leg adjacent ∠ A to the length of hypotenuse. cos A=Adjacent/Hypotenuse ⇒ cos A =4.3/9.1 By the definition of the inverse cosine, the inverse cosine of 4.39.1 is the measure of ∠ A. To find it, we have to use a calculator.

To find m∠ B, recall that the acute angles of a right triangle are complementary. Therefore, m ∠ A and m ∠ B add up to 90^(∘). m ∠ A + m ∠ B = 90^(∘) Now, we can substitute the approximated measure of ∠ A in our equation and find the measure of ∠ B. 61.8 ^(∘)+ m ∠ B ≈ 90^(∘) ⇔ m ∠ B ≈ 28.2^(∘)

Side Lengths

Finally, we can find the measure of a. To do it, we can use the Pythagorean Theorem. a^2 + b^2 = c^2 Let's substitute the known lengths, b = 4.3 and c= 9.1, into this equation to find a.