Question

the figure is not drawn to scale.
right triangle with legs 36 (side a) and 48, hypotenuse 60, angle b at the top vertex
answer
options:
\\(\frac{36}{60}\\)
\\(\frac{48}{60}\\)
\\(\frac{36}{48}\\)
\\(\frac{48}{36}\\)

Explanation:

Step1: Identify the sides for angle B

In a right - triangle, for an acute angle, the sine of the angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. For angle B, the opposite side to angle B has a length of 36, and the hypotenuse has a length of 60.

Step2: Calculate the sine of angle B

Using the definition of sine, \(\sin(B)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{36}{60}\)

Answer:

\(\frac{36}{60}\) (the first option among the given options)