Question

find the value of z. round to the nearest tenth
triangle with right - angle, one side = 5, one angle = 48 degrees
o 3.7
o 5.6
o 4.5
o 3.3

Explanation:

Step1: Use tangent function

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 48^{\circ}$ and the adjacent side to the angle $\theta$ is 5, and the opposite side is $x$. So $\tan48^{\circ}=\frac{x}{5}$.

Step2: Solve for $x$

We know that $\tan48^{\circ}\approx1.1106$. Then $x = 5\times\tan48^{\circ}$. Substituting the value of $\tan48^{\circ}$, we get $x=5\times1.1106 = 5.553\approx5.6$.

Answer:

5.6