Using a 30-60-90 triangle, if b = 12, find c?
I can't seem to get any formulas to work for this. any help would be wonderful.
In a 30-60-90 triangle, the shortest side is half the longest side, because sin(30°)=1/2.
We do not know what a,b and c stand for, namely which one is hypotenuse.
C is hypotenuse
To find the value of side c in a 30-60-90 triangle when side b is given, we can use the ratios of the sides in this special triangle.
In a 30-60-90 triangle, the ratio of the sides is as follows:
- The length of the side opposite the 30-degree angle is equal to half the length of the hypotenuse (c).
- The length of the side opposite the 60-degree angle is equal to the length of the hypotenuse (c) times the square root of 3.
- The length of the hypotenuse (c) is simply the length of the longest side.
Given that side b is 12, it corresponds to the side opposite the 60-degree angle. So, we can write the following equation:
b = c * √3
Substituting the value of b = 12 into the equation, we have:
12 = c * √3
To isolate c, we can divide both sides of the equation by √3:
12 / √3 = c
To rationalize the denominator of √3, we can multiply both the numerator and the denominator by √3:
(12 / √3) * (√3 / √3) = c
(12√3) / 3 = c
4√3 = c
Hence, the value of c in the 30-60-90 triangle, given that b = 12, is 4√3 or approximately 6.928.