Question

Find the length of MD to the nearest tenth.

Angle D is 50 degrees, angle M is 90 degrees, the opposite is 21

25
27.4
32.7
17.6

Answer 1

To find the length of \( MD \) in triangle \( M D N \) where angle \( D = 50^\circ \) and angle \( M = 90^\circ \), you can use the sine function since you are given the opposite side \( DN = 21 \).

The relationship involving the opposite side and the hypotenuse is given by:

\[
\sin(\text{Angle}) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

In this triangle, we have:

\[
\sin(50^\circ) = \frac{DN}{MD}
\]

Substituting the known values:

\[
\sin(50^\circ) = \frac{21}{MD}
\]

Now, we can solve for \( MD \):

\[
MD = \frac{21}{\sin(50^\circ)}
\]

First, calculate \( \sin(50^\circ) \):

\[
\sin(50^\circ) \approx 0.7660 \quad (\text{using a calculator})
\]

Now substituting that back into the equation for \( MD \):

\[
MD \approx \frac{21}{0.7660} \approx 27.4
\]

Thus, the length of \( MD \) to the nearest tenth is:

\[
\boxed{27.4}
\]