Question

b.u4l4 discussion_spr26

which function should the student use?
(1 point)

the student used the correct one.

sine

cosine

Explanation:

Step1: Recall trigonometric ratios

For an acute angle in a right triangle:
$\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$, $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Match sides to the 37° angle

For $\theta=37^\circ$, the side opposite is $x$, the adjacent side is not 9 (9 is the hypotenuse). The student misidentified the adjacent side; the correct ratio for opposite and hypotenuse is sine:
$\sin(37^\circ)=\frac{x}{9}$

Step3: Evaluate the student's error

The student incorrectly used tangent (confused hypotenuse with adjacent side). The correct function is sine.

Answer:

sine