Question

1. 11 64° x

Explanation:

Step1: Identify trigonometric relation

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 64^{\circ}$, the hypotenuse is 11 and the opposite side to the angle $64^{\circ}$ is $x$. So, $\sin64^{\circ}=\frac{x}{11}$.

Step2: Solve for $x$

Multiply both sides of the equation $\sin64^{\circ}=\frac{x}{11}$ by 11. We know that $\sin64^{\circ}\approx0.8988$. So, $x = 11\times\sin64^{\circ}\approx11\times0.8988 = 9.8868\approx9.89$.

Answer:

$x\approx9.89$