In ΔLMN, l = 6.9 cm, m = 8.1 cm and n=8.8 cm. Find the measure of ∠N to the nearest 10th of a degree.

Answer 1

Since this is a non-right triangle and all you have for information is the 3 sides, this is a situation where you will need to use the Law of Cosines to solve for the missing angle. The equation to set up for this, following the pattern for the Law of Cosines, is as follows:

n² = m² + l² - 2 m l cos N, so plugging in the numbers, we have:

8.8² = 8.1² + 6.9² - 2( 8.1)(6.9) cos N

Simplifying this, we have 77.44 = 113.22 - 111.78 cos N. We move the 113.22 to the other side by subtracting it to isolate the -111.78 cosN. So now we have -35.78 = -111.78 cos N. Now we divide both sides of the equation by -111.78 to isolate the cos N. When we do, we have cos N = 0.32. Now we use the inverse function for cos ( i.e. cos ^-1) on the calculator to determine that the measure of angle N is 71.3 degrees.

Answer 2

use the law of cosines

8.8^2=6.9^2+8.1^2-2*6.9*8.1*cosN

77.44=47.61+65.61-111.78cosN

77.44=113.22-111.78cosN

-35.78=-111.78cosN

-35.78/(-111.78)=cosN

0.320093=cosN

use inverse cos on your calculator or use the web

cos^-1N=0.320093

N=71.33145078°

N=71.3°, or...

N=71° 19' 53.223"

Answer 3

We can use the law of cosine to find ∠N.

a² = b² + c² - 2bc · cosA

Since we have the letters L, M, N and the objective is to find ∠N, we have

n² = l² + m² - 2lmcosN

Now, substitute the respective values.

8.8² = 6.9² + 8.1² - 2(6.9)(8.1)cosN

77.44 = 47.61 + 65.61 - 111.78cosN

Next, we will try to isolate cosine by subtracting 47.61 and 65.61 to both sides.

77.44 - 47.61 - 65.61 = -111.78cosN

-35.78 = -111.78cosN

Next, we will divide -111.78 to both sides.

-35.78 / (-111.78) = cosN

0.32009 = cosN.

Lastly, take the inverse cosine (ie cos^-1 OR arccos) of both sides.

N = cos^-1(0.32009) = 71.3º

*Please feel free to ask me any question for clarification.