Question

fall 2025 geometry b wwva solving for side lengths of right triangles what is the length of bc? round to the nearest tenth. 6.8 cm 17.7 cm 14.5 cm

Explanation:

Step1: Identify trigonometric ratio

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

Step2: Substitute values

We know that \(A = 65^{\circ}\) and \(AB = 16\) cm. So \(BC=AB\times\sin A\). Since \(\sin65^{\circ}\approx0.9063\), then \(BC = 16\times\sin65^{\circ}\).

Step3: Calculate the value

\(BC=16\times0.9063 = 14.5008\) cm.

Step4: Round to the nearest tenth

Rounding \(14.5008\) to the nearest tenth gives \(14.5\) cm.

Answer:

\(14.5\) cm