Question

Find c, the hypotenuse, rounded to four decimal places, in a right triangle with b = 16 and B = 55°.
(1 point)
Responses

11.2033
11.2033

19.5324
19.5324

22.6274
22.6274

27.8951

Answer 1

To find the hypotenuse \( c \) of a right triangle given that one side \( b = 16 \) (the side opposite angle \( B \)) and angle \( B = 55^\circ \), we can use the sine function from trigonometry:

\[
\sin(B) = \frac{\text{opposite}}{\text{hypotenuse}} \Rightarrow \sin(55^\circ) = \frac{b}{c}
\]

Rearranging the equation to solve for \( c \):

\[
c = \frac{b}{\sin(B)}
\]

Substituting in the known values:

\[
c = \frac{16}{\sin(55^\circ)}
\]

Now we need to calculate \( \sin(55^\circ) \). Using a calculator,

\[
\sin(55^\circ) \approx 0.8192
\]

Now substituting this value into the equation for \( c \):

\[
c = \frac{16}{0.8192} \approx 19.5324
\]

Finally, rounding to four decimal places, we get:

\[
c \approx 19.5324
\]

Thus, the value of \( c \), the hypotenuse, rounded to four decimal places is **19.5324**.