Question 444·Medium·Math

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In right triangle $ABC$ , angle $C$ is a right angle. The length of leg $AC$ is 6 centimeters and the length of hypotenuse $AB$ is 10 centimeters.

What is the value of $\sin B$ ?

A sine ratio in a right triangle compares the side opposite the chosen angle with the hypotenuse, the side across from the right angle. If both lengths are given, name those sides and write opposite over hypotenuse; you don't need the third side. The trap is choosing the wrong leg because you looked from a different angle.

Hints

Hint 1
The hypotenuse is across from the right angle and stays the same whichever acute angle you use. Stand at angle $B$ : which given leg lies across from it?
Hint 2
Sine means opposite divided by hypotenuse. Once you've named those sides from angle $B$ , put the opposite leg on top and the hypotenuse on the bottom. Which given lengths fill those spots?

Step-by-step

Name the sides from angle $B$
Step 1
Identify the opposite side and hypotenuse
No Desmos needed. Both sides for the ratio are given. Since $C$ is the right angle, $AB=10$ is the hypotenuse, the side across from it. From $B$ , $AC=6$ is the opposite leg, across from $B$ . The angle you're using decides which leg is opposite.
Step 2
Write the sine ratio
Use sine, the ratio of the opposite leg to the hypotenuse. Here those sides are $AC$ and $AB$ , so:
$\sin B=\frac{AC}{AB}=\frac{6}{10}.$
$BC$ touches $B$ , so it's the adjacent leg, not the opposite leg.
Step 3
Simplify the ratio
Divide the top and bottom by $2$ to simplify the fraction:
$\sin B=\frac{3}{5}.$
So the sine of angle $B$ is $\frac{3}{5}$ . Choice B.

Lessons that teach this

SAT Geometry and TrigonometryIntermediateCoreUse sine, cosine, and tangent

Question 444·Medium·Math

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Step-by-step

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