Question

1. the hypotenuse of the right triangle lmn shown below is 22 feet long. the cosine of angle l is \\(\frac{3}{4}\\). how many feet long is the segment lm?\

\
\
\
f. 18.4\
g. 16.5\
h. 11.0\
j. 6.7\
k. 4.7

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$. For angle \( L \), the adjacent side is \( LM \) (since \( M \) is the right angle, \( LM \) is one leg adjacent to \( L \)) and hypotenuse is \( LN = 22 \). So, $\cos(L) = \frac{LM}{LN}$.

Step2: Substitute known values

We know $\cos(L) = \frac{3}{4}$ and $LN = 22$. Substitute into the formula: $\frac{3}{4} = \frac{LM}{22}$.

Step3: Solve for \( LM \)

Multiply both sides by 22: $LM = 22 \times \frac{3}{4} = \frac{66}{4} = 16.5$.

Answer:

G. 16.5