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The hypotenuse of the right triangle ABC is 12.0 centimeters. The angle θ is 41.0 degrees. What is the length of the side opposite to angle θ? A. 7.87 centimeters B. 8.42 centimeters C. 12.4 centimeters
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The hypotenuse of the right triangle ABC is 12.0 centimeters. The angle θ is 41.0 degrees. What is the length of the side opposite to angle θ?

A.
7.87 centimeters
B.
8.42 centimeters
C.
12.4 centimeters
D.
23.4 centimeters

User StephenS
by
5.1k points

1 Answer

4 votes

Answer:

7.87 cm

Step-by-step explanation:

Trigonometry

SoH, CaH and ToA

You have the Hypotenuse and an angle. You're trying to find the length of the side opposite of the angle. So you are trying to find O.

This allows you to block out CaH and ToA because they don't have O and A in them at the same time.

Now you have only SoH

You are trying to find O. If you put SoH in a triangle like in the picture, you can cover up the O (because you're trying to find it) and see that you need to do S*H. S = angle and H = hypotenuse.

S= sin(41)

H = 12

O = sin(41) * 12 = 7.872 cm

Round to 2 d.p = 7.87 cm

The hypotenuse of the right triangle ABC is 12.0 centimeters. The angle θ is 41.0 degrees-example-1
User Elfif
by
4.7k points
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