Question

In AKLM, the Ineasure of ZM=90°, the measure of ZK=78°, and KL = 35 feet. Findthe length of MK to the nearest tenth of a foot.

Answer 1

We have the following right triangle:

then, using the cosine function, we have the following:

$\begin{gathered} \cos (78)=\frac{\text{adjacent side}}{hypotenuse}=\frac{MK}{35} \\ \Rightarrow\cos (78)=\frac{MK}{35} \end{gathered}$

solving for MK, we get:

$\begin{gathered} \frac{MK}{35}=\cos (78) \\ \Rightarrow MK=35\cdot\cos (78)=7.3 \\ MK=7.3ft \end{gathered}$

therefore, the length of MK is 7.3ft