find the measure of angle b in degrees. round to two decimal places as necessary. draw (triangle with right…

find the measure of angle b in degrees. round to two decimal places as necessary. draw (triangle with right angle, one leg 10, hypotenuse 27, angle b at the top)

find the measure of angle b in degrees. round to two decimal places as necessary. draw (triangle with right angle, one leg 10, hypotenuse 27, angle b at the top)

Answer

Explanation:

Step1: Identify sides relative to angle $b$

The side opposite angle $b$ is $10$, the hypotenuse is $27$.

Step2: Use sine function for angle $b$

$\sin(b) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{10}{27}$

Step3: Calculate inverse sine of the ratio

$b = \arcsin\left(\frac{10}{27}\right)$

Step4: Compute and round to 2 decimals

$b \approx \arcsin(0.3704) \approx 21.75^\circ$

Answer:

$21.75$ degrees