Question

Select the correct answer from each drop-down menu. Right triangle ABC is represented with the right angle at vertex B. Base BC measures 10 inches and angle C measures 40 degrees. In the figure, AB = inches and AC = inches.

Answer 1

By using trigonometric relations, we will see that:

AC = 15.6 in

AB = 8.4 in.

How to get the measures of the other two sides of the right triangle?

Here we have the right triangle where:

B = 90°

C = 40°

BC = 10 in.

Notice that is the adjacent cathetus to the angle C, then we can use the two relations:

• sin(a) = (adjacent cathetus)/(hypotenuse).
• tan(a) = (opposite cathetus)/(adjacent cathetus).

Where:

• hypotenuse = AC
• opposite cathetus = AB.

Then we will have:

sin(40°) = 10in/AC.

AC = 10in/sin(40°) = 15.6 in

tan(40°) = AB/10in

tan(40°)*10in = AB = 8.4 in.

So we can conclude that for the given right triangle we have:

AC = 15.6 in

AB = 8.4 in.

If you want to learn more about right triangles:

brainly.com/question/2217700

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