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Subject Test Math 1

Question 20 of 32

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SAT Subject Test

The figure presents right triangle A B C. Side A C is horizontal, side B C is vertical, and a right angle symbol is indicated at angle C. Below the figure is a note stating that the figure is not drawn to scale.

In the figure above, ▵ A B C has a right angle at C. If the length of side stack A C with bar on top is 10 and the measure of angle B A C is 22 degree, what is the length of side stack B C with bar on top invisible times?

Select an Answer

3.7

Correct Answer: 
No

4.0

Correct Answer: 
Yes

5.8

Correct Answer: 
No

6.8

Correct Answer: 
No

9.3

Correct Answer: 
No

The correct answer is B.

To determine the length of side stack B C with bar on top, apply the definition of the tangent of an angle theta in a right triangle: the tangent of theta is equal to the length of the side opposite angle theta divided by the length of the side adjacent to angle theta. Thus in this case, tan invisible times 22 degree equals fraction numerator B C over denominator A C end fraction equals fraction numerator B C over denominator 10 end fraction, which gives B C equals 10 tan invisible times 22 degree. Use a calculator, set to degree mode, to compute that 10 tan invisible times 22 degree almost equal to 4.0.

Question Difficulty: 
medium