Question 452·Easy·Math

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Which choice is equal to $\tan\theta$ for the triangle shown?

A right-triangle question asking for tangent is asking for a side-length ratio, not the angle itself. Start at the marked angle to identify the leg across from it and the leg touching it. Use opposite over adjacent. Reversing those legs flips the fraction; using the hypotenuse gives a different ratio.

Hints

Hint 1
The hypotenuse is the side across from the right angle, even though it also touches the marked acute angle. Set it aside for tangent. Which two sides are left?
Hint 2
Stand at $\theta$ to name the legs. The opposite leg is across from it, and the adjacent leg touches it. Tangent uses opposite over adjacent. Which labeled leg goes in each spot?

Step-by-step

Name the legs from the marked angle
Step 1
Set aside the hypotenuse
No Desmos needed. The figure labels both legs, so you can read their ratio directly. The right angle is at $C$ , so $AB=5$ , across from it, is the hypotenuse. Tangent doesn't use the hypotenuse.
Step 2
Name the legs from $\theta$
From $\theta$ at $A$ , $BC=3$ is across the triangle, so it's the opposite leg. $AC=4$ touches $A$ and isn't the hypotenuse, so it's the adjacent leg. Use $A$ , not $B$ , or you'll switch their roles.
Step 3
Write the tangent ratio
The tangent ratio is opposite leg over adjacent leg, so use the two legs you named: $\tan\theta=\frac{BC}{AC}=\frac{3}{4}$ . So $\tan\theta$ equals $\frac{3}{4}$ . Choice A.

Lessons that teach this

SAT Geometry and TrigonometryIntermediateCoreUse sine, cosine, and tangent

Question 452·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

Hints

Step-by-step

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