Question

What is the length of MN¯¯¯¯¯¯¯, to the nearest tenth of a foot? 10.6 ft 14.7 ft 15.6 ft 18.0 ft A horizontally-aligned scalene triangle M N P. Side M P is labeled as 10 feet. Side N P is labeled as 13 feet. Angle P is labeled as 78 degrees.

Answer 1

Using the Law of Cosine formula, you can find the measurement of the third side of a scalene or isosceles triangle. 

C^2 = A^2 + B^2  -  2AB(cosC)

C^2 = 10^2 + 13^2  -  2(10)(13)(cos78degrees)
C^2 = 100 + 169  -  2(10)(13)(cos78degrees)
C^2 = 100 + 169  -  2(10)(13)(0.21)
C^2 = 100 + 169  -  54.06
C^2 = 269  -  54.06
C^2 = 214.94
C^2 = square root of 214.94
C = 14.66

The answer for this question would be 14.7 ft. :D