How do you solve the triangle given a=4, b=8, c=5?

Question

3350 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-03T21:51:44

Please read the explanation for the steps leading to the measures the angles, $A = 24°, B = 125°, and C = 31°$

Use the Law of Cosines to find one of the angles (I choose angle B):

$b^2 = a^2 + c^2 - 2(a)(c)cos(B)$

$b^2 - a^2 - c^2 = -2(a)(c)cos(B)$

$cos(B) = (b^2 - a^2 - c^2)/( -2(a)(c))$

$B = cos^-1((b^2 - a^2 - c^2)/( - 2(a)(c)))$

$B = cos^-1((8^2 - 4^2 - 5^2)/( - 2(4)(5)))$

$B ~~ 125°$

Use the Law of Sines to find another angle (I choose angle A):

$sin(A)/a = Sin(B)/b$

$sin(A) = Sin(B)a/b$

$A = sin^-1(Sin(B)b/a)$

$A = sin^-1(Sin(125°)4/8)$

$A ~~ 24°$

Angle C is found by subtracting the angles A and B from 180°:

$C = 180 - 125 - 24$

$C = 31°$