A triangle has sides A, B, and C. Sides A and B have lengths of 10 and 8, respectively. The angle between A and C is (5pi)/24 and the angle between B and C is (3pi)/8. What is the area of the triangle?

1 Answer
SCooke
Jun 15, 2017

33

Explanation:

Degrees = (180/pi)*radians
(I just like working in degrees better)

Law of Cosines equation is c^2 = a^2 + b^2 – 2*a*b*cos(gamma).

The angle gamma needed is 180 – (37.5 + 67.5) = 180 - 105 = 75

c^2 = 10^2 + 8^2 – 2*10*8*cos(75).
c^2 = 100 + 64 – 160*(0.259).
c^2 = 122.6 : c = 11
Then using these values we can now find the height h for the triangle and solve for the area. sin(37.5) = h/10
h = sin(37.5) * 10 ; h = 6
A = (1/2)*b*h ; A = (1/2)*11*6 = 33

Related questions
See all questions in Area of a Triangle
Impact of this question
1536 views around the world
You can reuse this answer
Creative Commons License