Question

what is the length of bc? round to the nearest tenth.

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(ABC\) with \(\angle C = 90^{\circ}\), \(\angle A=65^{\circ}\), hypotenuse \(AB = 16\) cm, and we want to find the length of \(BC\) (opposite side to \(\angle A\)). Use the sine ratio: \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin A=\frac{BC}{AB}\).

Step2: Substitute the values

Substitute \(A = 65^{\circ}\) and \(AB = 16\) into the formula: \(\sin65^{\circ}=\frac{BC}{16}\).

Step3: Solve for \(BC\)

Multiply both sides by \(16\): \(BC = 16\times\sin65^{\circ}\).
Using a calculator, \(\sin65^{\circ}\approx0.9063\). Then \(BC=16\times0.9063 = 14.5008\).

Answer:

\(14.5\) cm