Question

1. opp adj 62 x hyp sinθ = opp/hyp sin62 = 2/x 1·2 = x·sin62 sin62 sin62 x =

Explanation:

Step1: Recall sine - ratio formula

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Given $\theta = 62^{\circ}$, the opposite side is 2 and the hypotenuse is $x$, so $\sin62^{\circ}=\frac{2}{x}$.

Step2: Cross - multiply

Cross - multiplying the equation $\sin62^{\circ}=\frac{2}{x}$ gives $x\sin62^{\circ}=2$.

Step3: Solve for $x$

Dividing both sides of the equation $x\sin62^{\circ}=2$ by $\sin62^{\circ}$, we get $x = \frac{2}{\sin62^{\circ}}$. Since $\sin62^{\circ}\approx0.8829$, then $x=\frac{2}{0.8829}\approx2.27$.

Answer:

$x\approx2.27$