We will find the missing measures one at a time. In this case, this means that we want to find m ∠ K, ML, and KL.
Angle Measures
To find m∠ K, recall that the acute angles of a right triangle are complementary. Therefore, m ∠ K and m ∠ M add to 90.
m ∠ K + m ∠ M = 90
Since we know the measure of ∠ M, we can substitute it in our equation and find the measure of ∠ K.
m ∠ K + 40 = 90 ⇔ m ∠ K = 50
Side Lengths
We can find the measure of ML and KL using sine and cosine ratios respectively.
The sine of ∠ K is the ratio of the length of the leg opposite ∠ K to the length of the hypotenuse.
Sine=Opposite/Hypotenuse ⇒ sin 50^(∘) =x/8
We can use the obtained equation to find the measure of ML. We have to use the calculator to find the value of the given sine. Then, we will substitute it into the equation and solve for x.
Therefore, the measure of ML is 6.1, rounded to nearest tenth. The cosine of ∠ K is the ratio of the length of the adjacent leg of ∠ K to the length of the hypotenuse.
Cosine=Adjacent/Hypotenuse ⇒ cos 50^(∘) =y/8
We can use the obtained equation to find the measure of KL. We have to use the calculator to find the value of the given cosine. Then, we will substitute it into the equation and solve for y.
