Question

a right triangle is given. determine the value for x. 5.7 11.7 6.3 9.8

Explanation:

Step1: Identify trigonometric ratio

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 40^{\circ}$, the opposite side to the $40^{\circ}$ angle is $7.5$ and the hypotenuse is $x$. So, $\sin40^{\circ}=\frac{7.5}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{7.5}{\sin40^{\circ}}$. Since $\sin40^{\circ}\approx0.6428$, then $x=\frac{7.5}{0.6428}\approx11.7$.

Answer:

$11.7$