GMAT Math : DSQ: Calculating the length of the side of a right triangle

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Example Question #143 : Triangles

$\bigtriangleup ABC$ is a right triangle with right angle $\angle B$ . Evaluate .

Statement 1: AC = 22 and $m \angle A = 30^{\circ }$ .

Statement 2: BC = 11 and $m \angle C = 60^{\circ }$ .

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Either statement alone is sufficient.

From either statement alone, it can be determined that $m \angle A = 30^{\circ }$ and $m \angle C = 60^{\circ }$ ; each statement gives one angle measure, and the other can be calculated by subtracting the first from $90^{\circ }$ , since the acute angles of a right triangle are complementary.

Also, since $\angle B$ is the right angle, $\overline{AC}$ is the hypotenuse, and $\overline{BC}$ , opposite the $30 ^{\circ }$ angle, the shorter leg of a 30-60-90 triangle. From either statement alone, the 30-60-90 Theorem can be used to find the length of longer leg $\overline{AB}$ . From Statement 1 alone, $\overline{AB}$ has length $\frac{\sqrt{3}}{2}$ times that of the hypotenuse, or $\frac{\sqrt{3}}{2} \cdot 22 = 11\sqrt{3}$ . From Statement 2 alone, $\overline{AB}$ has length $\sqrt{3}$ of the shorter leg, or $11\sqrt{3}$ .

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Example Question #2611 : Gmat Quantitative Reasoning

The longest side of a right triangle has a length of $13\textup{ in}$ . If the base of the triangle is $5\textup{ in}$ long, how long is the other side of the triangle?

Possible Answers:

$10\textup{in}$

$11\textup{in}$

$9\textup{in}$

$8\textup{in}$

$12\textup{in}$

Correct answer:

$12\textup{in}$

Explanation:

This is a Pythagorean theorem question. The lengths of a right triangle are related by the following equation: $a^{2}+b^{2}=c^{2}.$ In the problem statement, $c=13\textup{in}$ and $a=5\textup{in.}$ Therefore, $b^{2}= c^{2}-a^{2}= 13^{2}-5^{2}=169-25=144. b=\sqrt{144}=12\textup{in.}$

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GMAT Math : DSQ: Calculating the length of the side of a right triangle

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #143 : Triangles

Example Question #2611 : Gmat Quantitative Reasoning

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