Hey! so this is actually a really simple question if you memorized the 30 60 90 special triangle (search it up online, it'll help SO MUCH)
in general, using a as a variable, the hypotenuse is 2a, the shortest length (the length opposite the 30 degree angle) is a, and the other side (x, in this diagram) is a√3
Remark In a 30-60-90 triangle the opposite side and the hypotenuse of a 30 degree angle are in the ratio of 1:2. That means if the opposite side to a 30 degree angle is 5, then the hypotenuse should be 10.
Step one Solve for y ratio of 30 degree angle = opposite / hypotenuse
Givens opposite = 5 hypotenuse = x Ratio of 30 degree angle in a right triangle = 1/2
Sub and Solve 1/2 = opposite / hypotenuse 1/2 = 5 / hypotenuse Multiply both sides by hypotenuse 0.5 * hypotenuse = 5 Divide by 0.5 hypotenuse = 5/0.5 hypotenuse = 10
Step 2 Find x
Givens hypotenuse = 10 In a 30 - 60 - 90 triangle the ratio of the adjacent side to the hypotenuse = sqrt(3) / 2
Sub and solve sqrt(3)/2 = adjacent / hypotenuse sqrt(3) /2 = adjacent / 10 Multiply both sides by 10 10 * sqrt(3) / 2 = adjacent Cancel 5 * sqrt(3)
