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

Question

bearhunter [10]

3 years ago

13

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.

Mathematics

1 answer:

Dmitry_Shevchenko [17] · Answer 1 · 2022-06-08T23:37:00+03:00

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