Question

$ab = square$
round your answer to the nearest hundredth.
in right triangle $abc$, $angle c = 90^circ$, $angle a = 50^circ$, $bc = 6$, find the length of $ab$.

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with angle $\angle A = 50^\circ$, opposite side $BC = 6$, and hypotenuse $AB$ (unknown). Use the sine function:
$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(50^\circ) = \frac{6}{AB}$

Step3: Solve for $AB$

Rearrange to isolate $AB$:
$AB = \frac{6}{\sin(50^\circ)}$
Calculate $\sin(50^\circ) \approx 0.7660$, so:
$AB \approx \frac{6}{0.7660} \approx 7.83$

Answer:

$7.83$