Question

trig #1
find the missing side.
.07
6.2
7.53
8.22

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for angle \(B = 37^{\circ}\), the hypotenuse \(AB=10.3\) and the side \(AC = x\) (opposite to angle \(B\)). Use the sine ratio \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
So, \(\sin37^{\circ}=\frac{x}{10.3}\).

Step2: Solve for \(x\)

We know that \(\sin37^{\circ}\approx0.6\) (a common approximation).
Substitute \(\sin37^{\circ}\) into the equation: \(x = 10.3\times\sin37^{\circ}\).
\(x=10.3\times0.6\).
\(x = 6.18\approx6.2\).

Answer:

6.2