In right triangle ABC, angle C is the right angle and A = 513. What is the value of B?

SAT Right triangles and trigonometry Practice Question 1 (Medium)

SAT Owl

Question bank / Right triangles and trigonometry

Math · Geometry and TrigonometryMedium

In right triangle $ABC$ , angle $C$ is the right angle and $\sin A = \frac{5}{13}$ . What is the value of $\cos B$ ?

$\frac{12}{13}$

$\frac{5}{13}$

$\frac{12}{5}$

$\frac{13}{5}$

Show answer and explanation

Answer: B

$\sin A$ is the side opposite $A$ over the hypotenuse, so $BC = 5k$ and $AB = 13k$ . The side adjacent to angle $B$ is also $BC$ , so $\cos B = \frac{BC}{AB} = \frac{5}{13}$ . In general, the sine of one acute angle in a right triangle equals the cosine of the other.

Choice A is $\cos A$ , which uses the third side $AC = 12k$ rather than the side adjacent to $B$ .

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free.