Question

bc = \boxed{\space}
round your answer to the nearest hundredth.

(right triangle with right angle at c, angle at a is 50°, hypotenuse ab is 3, bc is unknown (marked as ?))

1 / 4 the strategy

1. note that we are given the length of the hypotenuse, and we are asked to find the side opposite to the given angle. the trigonometric ratio that contains both of those sides is

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle with hypotenuse \( AB = 3 \), angle \( A = 50^\circ \), and we need to find \( BC \) (opposite to angle \( A \)). The sine ratio is \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). So, \( \sin(50^\circ)=\frac{BC}{3} \).

Step2: Solve for \( BC \)

Multiply both sides by 3: \( BC = 3\times\sin(50^\circ) \). Calculate \( \sin(50^\circ)\approx0.7660 \), so \( BC\approx3\times0.7660 = 2.298 \). Round to nearest hundredth: \( BC\approx2.30 \).

Answer:

\( 2.30 \)