Question

Solve for x and y in radical form

Answer 1

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

therefore, for this diagram:
y=10
x=5√3

hope this helps!

Answer 2

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)