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Use Pythagorean to solve a right triangle problem
Question:
ABC is a right triangle with the angle C is 90o. If the angle B is 30o, what is the length of AC?
right triangle example when one angle is 30 degree.
Solution:
let the length of AC be x, that is, AC = x
since ABC is a right triangle (Given), the angle B is 30o witch opposite AC
since AB is the hypotenuse of the right triangle, and the angle B is 30o and it opposite AC
so AB = 2 AC
since in a right triangle, the side opposite 30o is one-half the hypotenuse.
so AB = 2 AC = 2x
Pythagorean theorem: the square of the hypotenuse is equal to the sum of the square of two legs.
that is, AB2 = AC2 + BC2
Given: BC = 3 feet
(2x)2 = x2 + 32
4x2 = x2 + 9
move the variable to the left side of the equation
4x2 - x2 = 9
3x2 = 9
divide by 3 in both side of the equation
x2 = 3
since x is the length of AC, so x must be possitive
so x = square root of 3.
so the length of AC is square root of 3 feet.