Question

How do you solve the right triangle given b = 4, B = 10 degrees?

Answer 1

`color(brown)(a = 22.69, c = 23.04, hat A = 80^@, A_t = 45.38 " sq units"`

Explanation:

`"it's a right triangle with " b = 4, hat B = 10^@`

`hat A = 180 - 90 - 10 = 80^@`

Applying Law of Sines,

`a / sin A = b / sin B = c / sin C`

`a = (b sin A) / sin B = (4 * sin 80) / sin 10 = 22.69`

`c = (b sin C) / sin B = (4 * sin 90) / sin 10 = 23.04`

Verification by applying Pythagoras theorem,

`c = sqrt(a^2 + b^2) = sqrt(22.69^2 + 4^2) = 23.04`

`"Area of the rt triangle " A_t = (1/2) * a * b = (1/2) * 22.69 * 4 = 45.38`