Question

b = \boxed{} round your answer to the nearest hundredth. triangle diagram: right - angled at c, angle at a is 50°, side bc = 6, hypotenuse ab marked ?

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \(ABC\) with \(\angle C = 90^\circ\), \(\angle A = 50^\circ\), and \(BC = 6\) (opposite to \(\angle A\)), we need to find the hypotenuse \(AB\). We use the sine function: \(\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin(50^\circ)=\frac{BC}{AB}\).

Step2: Solve for \(AB\)

Rearrange the formula: \(AB = \frac{BC}{\sin(50^\circ)}\). Substitute \(BC = 6\) and \(\sin(50^\circ)\approx0.7660\): \(AB=\frac{6}{0.7660}\approx7.83\).

Answer:

\(7.83\)