Exercise 40 Page 925

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 a, b, and m ∠ B.

Side Lengths

We can find a using a sine ratio.

The sine of ∠ A is the ratio of the length of the leg opposite ∠ A to the length of the hypotenuse. We know that a is equal to the length of the leg opposite ∠ A, and therefore we can write the following equation. Sine=Opposite/Hypotenuse ⇒ sin 52 ^(∘) =a/10 To solve this equation, we will first isolate a. Then, we will have to use the calculator to find the value of sin 52 ^(∘).

Now, we can find b using the Pythagorean Theorem. a^2 + b^2 = c^2 Let's substitute the known lengths, a = 7.9 and c= 10, into this equation to find b.

Angle Measures

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 measure of ∠ A in our equation and find the measure of ∠ B. 52^(∘) + m ∠ B = 90^(∘) ⇔ m ∠ B =38.0^(∘)