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Subject Test Math 1

Question 11 of 32

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SAT Subject Test

The figure presents right triangle P Q R. Side P R is horizontal, side P Q is vertical, and there is a right angle symbol at angle P. Angle R is labeled “theta.”

In the figure above, if fraction numerator P Q over denominator Q R end fraction invisible times equals fraction numerator 2 over denominator 3 end fraction, then tan invisible times theta invisible times equals

Select an Answer

2 over 5

Correct Answer: 
No

fraction numerator 2 over denominator square root of 5 end fraction

Correct Answer: 
Yes

fraction numerator 3 over denominator square root of 5 end fraction

Correct Answer: 
No

fraction numerator square root of 5 over denominator 2 end fraction

Correct Answer: 
No

fraction numerator square root of 5 over denominator 3 end fraction

Correct Answer: 
No

The tangent of an acute angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. You can find the length of the adjacent side P R by using the Pythagorean Theorem. Using the given information, let the length of P Q be 2 and the length of Q R be 3. Then, left parenthesis P Q right parenthesis to the power of 2 end exponent invisible times plus left parenthesis P R right parenthesis to the power of 2 end exponent invisible times equals left parenthesis Q R right parenthesis to the power of 2 end exponent or 4 invisible times plus left parenthesis P R right parenthesis to the power of 2 end exponent invisible times equals 9.

Thus P R invisible times equals square root of 5 end root and tan theta invisible times equals fraction numerator P Q over denominator P R end fraction invisible times equals fraction numerator 2 over denominator square root of 5 end root end fraction.
The correct answer is (B).

Question Difficulty: 
medium