Question

1. solve for each indicated side length a) b)

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 28^{\circ}$, the opposite side is $x$, and the hypotenuse is $10$ cm. So, $\sin28^{\circ}=\frac{x}{10}$.

Step2: Solve for $x$

Multiply both sides of the equation $\sin28^{\circ}=\frac{x}{10}$ by $10$. We know that $\sin28^{\circ}\approx0.4695$. Then $x = 10\times\sin28^{\circ}$. Substituting the value of $\sin28^{\circ}$, we get $x\approx10\times0.4695 = 4.695$ cm.

Answer:

$x\approx4.7$ cm (rounded to one decimal place)