Question

find the value of x. round to the nearest tenth.
5
48°
o 3.7
5.6
o 4.5
o 3.3

Explanation:

Step1: Identify trigonometric relation

In a right - triangle, we know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 48^{\circ}$, the adjacent side to the angle 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 $x=5\times1.1106 = 5.553$.

Step3: Round to the nearest tenth

Rounding 5.553 to the nearest tenth gives 5.6.

Answer:

5.6