Exercise 43 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 ∠ A.

Side Lengths

We can find b using a sine ratio.

The sine of ∠ B is the ratio of the length of the leg opposite ∠ B to the length of the hypotenuse. We know that b is equal to the length of the leg opposite ∠ B and that 20 is equal to the length of the hypotenuse. Therefore, we can write the following equation. sin B=Opposite/Hypotenuse ⇒ sin 8.3 ^(∘) =b/20 To solve this equation, we will first isolate b. Then, we will have to use the calculator to find the value of sin 8.3 ^(∘).

Now, we can find a using the Pythagorean Theorem. a^2 + b^2 = c^2 Let's substitute the known lengths, b = 2.9 and c= 20, into this equation to find a.

Angle Measures

To find m∠ A, 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 ∠ B in our equation and find the measure of ∠ A. m ∠ A+8.3^(∘) = 90^(∘) ⇔ m ∠ A =81.7^(∘)