Question

Find the length of MD to the nearest tenth
Imagine a right triangle. The point on the left is labelled V, the point on the right of it is labelled M, and the point below that is labelled D.
Line VM is labelled 21, and inside the triangle near Point D is angle 50.

Answer 1

To find the length of \( MD \) in the right triangle \( VMD \) where \( V \) is the top vertex, \( M \) is the bottom right vertex, and \( D \) is the bottom left vertex, we can use trigonometric functions.

In the triangle, we have:
- \( VM = 21 \) (the length of the vertical side opposite angle \( D \))
- \( \angle VMD = 50^\circ \)

Since we want to find the length \( MD \), we can utilize the cosine function, which relates the adjacent side \( MD \) to the hypotenuse \( VM \):

\[
\cos(\angle VMD) = \frac{MD}{VM}
\]

Substituting the known values:

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

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

\[
MD = 21 \cdot \cos(50^\circ)
\]

Using a calculator to find \( \cos(50^\circ) \):

\[
\cos(50^\circ) \approx 0.6428
\]

Substituting this into the equation for \( MD \):

\[
MD \approx 21 \cdot 0.6428 \approx 13.5
\]

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

\[
\boxed{13.5}
\]