In triangle MNP, side m is 54.5 inches, side n is 51.4 inches, and side p is 60 inches long. What is the measure of P?

P = 68.95

Step-by-step explanation:

Here, we want to get the measure of angle P

Please check the attachment for the diagram of the triangle

To get P, we use the cosine rule

p^2 = m^2 + n^2 - 2mn Cos P

60^2 = 51.4^2 + 54.5^2 -2(51.4)(54.5) Cos P

2012.21 = 5602.6 Cos P

cos P = 2012.21/5602.6

cos P = 0.3592

P = arc cos 0.3592

P = 68.95

step-by-step explanation:

consider the parallelogram shown in the attached image.

in the parallelogram hijk, the length of hk is given as,

from the properties of parallelogram we know that the opposite sides of a parallelogram are parallel to each other and are equal in measure.

therefore, the length of the side ij must be equal to the length of the side hk and that is .

hence, the expression for the length of ij confirms that hijk is a parallelogram.