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Subject Test Math 1

Question 20 of 32

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 $\bar{A C}$ is $10$ and the measure of $∠ B A C$ is $22 °$ , what is the length of side $\bar{B C}$ ?

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$3.7$

Correct Answer:

No

$4.0$

Correct Answer:

Yes

$5.8$

Correct Answer:

No

$6.8$

Correct Answer:

No

$9.3$

Correct Answer:

No

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The correct answer is B.

To determine the length of side $\bar{B C}$ , apply the definition of the tangent of an angle $θ$ in a right triangle: the tangent of $θ$ is equal to the length of the side opposite angle $θ$ divided by the length of the side adjacent to angle $θ$ . Thus in this case, $\tan 22 ° = \frac{B C}{A C} = \frac{B C}{10}$ , which gives $B C = 10 \tan 22 °$ . Use a calculator, set to degree mode, to compute that $10 \tan 22 ° \approx 4.0$ .

Question Difficulty:

medium

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Subject Test Math 1

Question 20 of 32

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