Question

If the hypotenuse of a right triangle is 15.3m and the angle are 41 degrees and 49 degrees, what is the length of the leg opposite the 49 degree angle?

Answer 1

By definition, the sine of an angle in a right triangle is:

$$\sin\alpha = \dfrac{\text{opposite leg}}{\text{hypotenuse}}$$

Taking $\alpha = 49\degree$, and $\text{hypotenuse} = 15.3m$ obtain the opposite leg:

$$\text{opposite leg} = 15.3m\cdot \sin{49\degree} \approx 11.55m$$

Answer. 11.55 m.