Question

A.
x = 10/3, y = 30
b. x= 10, y = 30-3
c. x= 30/3, y=10
d. x = 30, y = 10.73

Answer 1

d.
`\displaystyle x = 30, y = 10√(3)`

Explanation:

In a 30°-60°-90° triangle, the shorter leg is represented by
`\displaystyle x,`the longer leg is represented by
`\displaystyle x√(3),`and the hypotenuse is represented by
`\displaystyle 2x.` So, evaluate:

`\displaystyle hypotenuse \hookleftarrow 2x \\ long\:leg \hookleftarrow x√(3) \\ short\:leg \hookleftarrow x \\ \\ 20√(3) = 2x\:[x\:is\:'y'\:in\:this\:case]; 10√(3) \\ \\ \\ x√(3) = x \\ \\ 30 = 10√(3)[√(3)]`

In the end, you arrive at this:

`\displaystyle x = 30, y = 10√(3)`

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