Question

Solve the right triangle ABC with right angle C if B=30 degrees and c=10.

a=5, b=5, A=60 degrees
a=5, b≃ 8.6602, A=60 degrees
a≃5.7735, b≃11.5470, A=60 degrees
a≃8.6602, b=5, A=60 degrees

Answer 1

aâ‰8.6602, b=5, A=60 degrees Let's calculate the lengths of the sides and angles and see what option fits. Since the sum of the angles in a triangle equals 180 and we known 2 of the angles, let's calculate angle A first. A = 180 - 90 - 30 = 60 Now for side b. This is a 30/60/90 triangle. The side opposite B is half the length of c since if you were to reflect the triangle across side a, you would have an equilateral triangle. So b is 10/2 = 5. And finally, since we have a right triangle, we can use the Pythagorean theorem to get the remaining side a. So a = sqrt(10^2 - 5^2) = sqrt(100 - 25) = sqrt(75) = 5*sqrt(3) ≠8.660254038 And of the available choices, only the last one matches which is aâ‰8.6602, b=5, A=60 degrees As a side note, the last option comes close, but isn't entirely correct since the properly rounded value for a should be 8.6603, not 8.6602.

Answer 2

c=10, C=90°, B=30°, A+B+C=180°
A+30°+90°=180°⇒A=60°

cos30°=a/c
cos30°=a/10⇒a=cos30°*10
a≃8.6602


c²=a²+b²⇒b²=c²-a²
b²=10²-8.6602²⇒b²=25
b=5