Question

How do you solve the triangle given `triangleDEF, d=36, e=72, mangleD=30`?

Answer 1

`color(blue)(f = 36sqrt3, hat F = 60^@, hat E = 90^@`

Explanation:

`color(blue)(d = 36, hat D = 30, e = 72`

Applying law of sines,

`hatE = sin ^-1 ((sin D * e) / d) = sin ^-1 ((sin 30 * 72)/36) = 90^@`

`hat F = 180 - 30 - 90 = 60^@`

It’s a right triangle with angles `30, 60, 90`

`:. f = sqrt3 * 36 = 62.3538`