find ( mangle b ).\n\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n(…

Explanation:

Step1: Identify sides for angle B

In right $\triangle BCD$, $\angle C=90^\circ$. For $\angle B$, adjacent side $BC$ is unknown, opposite side $CD=6$, hypotenuse $BD=7$.

Step2: Use sine function for angle B

Sine of angle is $\frac{\text{opposite}}{\text{hypotenuse}}$. $\sin(\angle B) = \frac{CD}{BD} = \frac{6}{7}$

Step3: Calculate angle B

Take inverse sine to find $\angle B$. $\angle B = \arcsin\left(\frac{6}{7}\right)$ Using a calculator, $\arcsin\left(\frac{6}{7}\right) \approx 59.0^\circ$

Answer:

$59.0$