Find the known measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.

KM = 10.68

K = 55 degrees

M = 35 degrees

Step-by-step explanation:

Firstly, we can use Pythagoras’ theorem to calculate the length of the hypotenuse which is KM

Mathematically, this is the sum of the squares of the two other sides KL and LM according to Pythagoras’ theorem

Thus, we have it that;

KM^2 = KL^2 + LM^2

KM^2 = 6.2^2 + 8.7^2

KM^2 = 114.13

KM = √(114.13)

KM = 10.68

We have two angles to calculate

Let us start with the angle at vertex K

The opposite side to is is the length LM which is 8.7

The adjacent side to it is the length 6.2

Mathematically, the relationship between the two can be calculated using the Tan ; as the Tan of an angle is the ratio of the length of the opposite to that of the adjacent

thus;

Tan K = 8.7/6.2

K = arc Tan (8.7/6.2)

K = 54.5 which is 55 degrees

since we have a right angle , we only have to subtract he measure of angle K from 90 to get the measure of M

M = 90-55 = 35 degrees