Question

question 11 of 12
what is \\(\sin 74^\circ\\)?

triangle image with angles 16°, 74°, 90° and sides 24, 7, 25

a. \\(\frac{24}{25}\\)
b. \\(\frac{7}{25}\\)
c. \\(\frac{7}{24}\\)
d. \\(\frac{24}{7}\\)

Explanation:

Step1: Recall sine definition

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

Step2: Identify sides for $74^\circ$

Opposite side = 24, hypotenuse = 25

Step3: Calculate $\sin74^\circ$

$\sin74^\circ = \frac{24}{25}$

Answer:

A. $\frac{24}{25}$