Question

I need help quickly, I'm preparing for a test! Help is appreciated!

Answer 1

The measure of angle ∠A and angle ∠C will be 65.37° and 17.63°. And the measure of the length of CA will be 29.48 inches.

What is trigonometry?

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

In triangle ABC, the side AB is 9 in, the side BC is 27 in, and the angle B is 97 degrees.

Then the other two angles and the side CA will be

The side CA is given by the cosine rule. Then we have

$\rm CA^2 = AB ^2+ BC^2 - 2 \times AB \times BC \cos B\\\\\\CA^2 = 9^2 + 27^2 - 2 \times 9 \times 27 \cos 97^o\\\\\\CA^2 = 810 + 59.23\\\\\\CA ^2 = 869.23\\\\\\CA \ = 29.48 \ in$

Then angle A will be given by the sine rule. Then we have

$\dfrac{27}{\sin A} = \dfrac{29.48}{\sin 97^0}\\\\\\\sin A = \dfrac{27 \sin 97^0}{29.48}\\\\\\\sin A = 0.9090\\\\\\A \ \ \ \ = 65.37^0$

Then the angle C will be

     ∠A + ∠B + ∠C = 180°

65.37° + 97° + ∠C = 180°

                       ∠C = 17.63°

More about the trigonometry link is given below.

brainly.com/question/22698523

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