Question

find the length of the hypotenuse to the nearest tenth.
right triangle abc with right angle at c, bc = 14, angle at a is 33°

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(ABC\), \(\angle C = 90^\circ\), \(\angle A = 33^\circ\), and \(BC = 14\) (opposite to \(\angle A\)). We use the sine ratio: \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin 33^\circ=\frac{BC}{AB}\).

Step2: Solve for hypotenuse \(AB\)

Rearrange the formula: \(AB = \frac{BC}{\sin 33^\circ}\). Substitute \(BC = 14\) and \(\sin 33^\circ\approx0.5446\): \(AB=\frac{14}{0.5446}\approx25.7\).

Answer:

\(25.7\)