Question 476·Easy·Math

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In right triangle $PQR$ , $\angle Q$ is a right angle. The length of side $PQ$ is $9$ units, and the length of side $PR$ is $15$ units.

What is the value of $\cos P$ ?

A cosine ratio compares the leg next to an acute angle with the hypotenuse, the side across from the right angle. Identify the hypotenuse first, then find the adjacent leg from the angle named in the question. Cosine is adjacent over hypotenuse. The tempting slip is to put the other leg in the denominator.

Hints

Hint 1
The hypotenuse is always across from the right angle. The right angle is at $Q$ , so which side is across from $Q$ ?
Hint 2
The adjacent leg touches the angle you're using but isn't the hypotenuse. From $P$ , which leg fits that description? Put its length over the hypotenuse to form the cosine ratio.

Step-by-step

Identify the sides and use cosine
Step 1
Find the hypotenuse
No Desmos needed. The cosine ratio uses the two given sides directly. The hypotenuse is across from the right angle. Since $\angle Q$ is right, $PR=15$ is the hypotenuse.
Step 2
Find the leg adjacent to $P$
From $\angle P$ , $PQ$ touches the angle and isn't the hypotenuse, so $PQ=9$ is the adjacent leg. Don't use $PR$ as the adjacent leg because it touches $P$ ; it has a different role as the hypotenuse.
Step 3
Form and reduce the cosine ratio
Use cosine, adjacent over hypotenuse, with the sides you identified:
$\cos P=\frac{PQ}{PR}=\frac{9}{15}.$
Divide the numerator and denominator by $3$ :
$\cos P=\frac{3}{5}.$
So the value of $\cos P$ is $\frac{3}{5}$ . Choice C.

Lessons that teach this

SAT Geometry and TrigonometryIntermediateCoreUse sine, cosine, and tangent

Question 476·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

Hints

Step-by-step

Lessons that teach this