Question

Find the length of MD to the nearest tenth (1 point) Responses 25 25 27.4 27.4 32.7 32.7 17.6 (One side is 21, there is a angle that's 50 degrees, and a 90 degree angle)

Answer 1

To find the length of \( MD \) in the given triangle with side lengths and angles, we can use the information provided: one side of length 21, an adjacent angle of 50 degrees, and the other angle is 90 degrees.

We can apply the trigonometric functions based on the triangle configuration. Assuming \( M \) is the vertex at the 90-degree angle, and the side of length 21 is adjacent to the angle of 50 degrees (let's label the sides), we can denote:

- \( MA \) is the side adjacent to the 50-degree angle, therefore \( MA = 21 \).
- \( MD \) is the side opposite the 50-degree angle.

Using the tangent function:
\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\]
\[
\tan(50^\circ) = \frac{MD}{21}
\]

Now we can solve for \( MD \):
\[
MD = 21 \cdot \tan(50^\circ)
\]

Calculating \( \tan(50^\circ) \):
\[
\tan(50^\circ) \approx 1.1918
\]

Now plug this into the equation:
\[
MD \approx 21 \cdot 1.1918 \approx 25.0318
\]

Rounding to the nearest tenth gives:
\[
MD \approx 25.0
\]

Thus, the length of \( MD \) to the nearest tenth is:
\[
\boxed{25.0}
\]