Question 584·Easy·Math

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In right triangle $RST$ , $\angle S$ is the right angle. If $RS = 8$ units and $ST = 15$ units, what is $\tan R$ ?

The cue for a tangent ratio is a right triangle with two known legs and an acute angle named. Stand at that angle: the leg across from it is opposite, and the leg touching it is adjacent. Divide opposite by adjacent. Don't swap the legs or use the hypotenuse; neither is needed to find tangent.

Hints

Hint 1
The hypotenuse is across from the right angle. Set it aside: tangent compares the other two sides, called legs. From $\angle R$ , which leg is across the triangle?
Hint 2
The opposite leg lies across from your angle, and the adjacent leg touches it. Tangent puts opposite on top. Which of $ST$ and $RS$ belongs in the numerator?

Step-by-step

Name the legs, then use tangent
Step 1
Identify the legs from angle R
No Desmos needed. Tangent uses the two given legs directly. The right angle is at $S$ , so $RT$ is the hypotenuse, the side across from the right angle. From $\angle R$ , $ST=15$ is the opposite leg across the triangle; $RS=8$ is the adjacent leg touching $R$ . Name the legs from the angle you're asked about.
Step 2
Write the tangent ratio
The tangent of an angle is its opposite leg divided by its adjacent leg, so opposite goes on top:
$\tan R=\frac{ST}{RS}=\frac{15}{8}.$
So $\tan R$ is $\frac{15}{8}$ . The hypotenuse doesn't enter this ratio. Choice B.

Lessons that teach this

SAT Geometry and TrigonometryIntermediateCoreUse sine, cosine, and tangent

Question 584·Easy·Math

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Strategy

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