Question

In a right triangle, if the lengths of the opposite and adjacent sides are 7 and 24 respectively, find sin $\theta$.

• A. 7/25
• B. 24/25
• C. 7/24
• D. 24/7

Answer 1

Answer: (A)

7/25

Answer 2

To find $\sin \theta$, we need to determine the ratio of the opposite side to the hypotenuse in the right triangle.

1. Find the hypotenuse (H): Using the Pythagorean theorem: $H^2 = Opposite^2 + Adjacent^2$ $H^2 = 7^2 + 24^2 = 49 + 576 = 625$ $H = \sqrt{625} = 25$

2. Calculate $\sin \theta$: $\sin \theta = \frac{Opposite}{Hypotenuse} = \frac{7}{25}$

Therefore, $\sin \theta = \frac{7}{25}$.