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 we have a right angle.)
Answers
GPT-4o mini
To find the length of MD given that one side is 21 and there is a 50-degree angle in a right triangle, we can apply the trigonometric functions.
Assuming the side of length 21 is adjacent to the 50-degree angle, we can use the cosine function:
\[
\cos(50^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]
Let \( \text{hypotenuse} = MD \):
\[
\cos(50^\circ) = \frac{21}{MD}
\]
Rearranging the equation gives:
\[
MD = \frac{21}{\cos(50^\circ)}
\]
Calculating \( \cos(50^\circ) \):
\[
\cos(50^\circ) \approx 0.6428
\]
Now substituting that into the equation:
\[
MD \approx \frac{21}{0.6428} \approx 32.7
\]
Therefore, the length of MD to the nearest tenth is:
\[
\boxed{32.7}
\]
Assuming the side of length 21 is adjacent to the 50-degree angle, we can use the cosine function:
\[
\cos(50^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]
Let \( \text{hypotenuse} = MD \):
\[
\cos(50^\circ) = \frac{21}{MD}
\]
Rearranging the equation gives:
\[
MD = \frac{21}{\cos(50^\circ)}
\]
Calculating \( \cos(50^\circ) \):
\[
\cos(50^\circ) \approx 0.6428
\]
Now substituting that into the equation:
\[
MD \approx \frac{21}{0.6428} \approx 32.7
\]
Therefore, the length of MD to the nearest tenth is:
\[
\boxed{32.7}
\]