Question

which of the following expressions is equal to the height, h, of this triangle? a. 25(cos34°) b. 25(cos56°) c. 25(tan34°) d. 25(tan56°) please select the best answer from the choices provided

Explanation:

Step1: Recall sine - cosine - tangent relations

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the hypotenuse is 25 ft and the angle is $34^{\circ}$, and we want to find the height $h$ (opposite side to the $34^{\circ}$ angle).
We know that $\sin34^{\circ}=\frac{h}{25}$, so $h = 25\sin34^{\circ}$. Also, since $\sin\theta=\cos(90^{\circ}-\theta)$, then $\sin34^{\circ}=\cos(90 - 34)^{\circ}=\cos56^{\circ}$, so $h=25\cos56^{\circ}$.

Answer:

B. $25(\cos56^{\circ})$