What is the length of leg b if leg a is 5 in a 30-60-90 triangle?

Answer 1

Since you wrote 30-60-90, that is angle A is 30 degrees, and opposite the angle A is the side a = 5, the angle B = 60 degrees, and opposite the angle B is the side b, the angle C = 90 degrees, and opposite the angle C is the side c. In a right triangle, where an acute angle is 30 degrees, the length measure of the side opposite to 30 degrees angle is equal to the one half of the length measure of the hypotenuse. That is 2a = (2)(5) = 10 = c. By using the Pythagorean theorem, c^2 = a^2 + b^2, we can say that:

b^2 = c^2 - a^2

b^2 = 10^2 - 5^2

b^2 = 100 - 25

b^2 = 75

b = square root of 75

b = 8.66

b = 8.7

or you can use the Law of Sine:

a/sinA = b/sinB

5/sin 30 = b/sin 60

b = [5(sin 60)]/sin 30

b = 8.66

b = 8.7