Question

How do you solve the right triangle ABC given fC = 90 degrees, B = 20 degrees, and b= 10 ?

Answer 1

`color(indigo)(hat(A) = 70^@, a = 27.47, c = 29.23, "Area of Right " Delta = 137.35`

Explanation:

`hat C = 90^@, hat B = 20^@, color(brown)(hat A =) 180 - 90 - 20 = color(brown)(70^@), b = 10`

Applying the Law of Sines,

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

`a = (b * sin A) / sin B = (10 * sin 70) / sin 20 = 27.47`

Applying Pythagoras Theorem,

`"Hypotenuse " = c = sqrt (a^2 + b^2) = sqrt((27.47^2 + 10^2)) = 29.23`

`"Area of Right " Delta = (1/2) * a * b = (1/2) * 27.47 * 10 = 137.35`