How do you find the measure of each of the angles of a triangle given the measurements of the sides are 9, 10, 15?

Question

1550 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-26T15:16:45

$color(blue)(hat A = 35.58^@, hat B = 40.27^@, hat C = 104.15^@)$

$a = 9, b = 10, c = 15$

enter image source here

Applying law of Cosines,

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

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

$cos C = (9^2 + 10^2 - 15^2) / (2 * 9 * 10) = - 0.2444$

$hat C = cos ^-1 (-0.2444) = 104.15^@$

Applying law of sines,

enter image source here
$hat A = sin ^-1 ((sin C * a) / c) = sin ^-1 (sin 104.15 * 9) / 15 = 35.58^@$

$hat B = 180 - 104.15 - 35.58 = 40.27^@$