Question

ab = \square
round your answer to the nearest hundredth.
(there is a right triangle abc with right angle at c, angle at a is 50 degrees, length of bc is 6, and ab is the hypotenuse with a? mark)

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(A) = \frac{BC}{AB}$

Step2: Rearrange to solve for AB

$AB = \frac{BC}{\sin(A)}$

Step3: Substitute given values

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

Step4: Calculate and round

$\sin(50^\circ) \approx 0.7660$, so $AB \approx \frac{6}{0.7660} \approx 7.83$

Answer:

7.83