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

Answer:

d. $\displaystyle x = 30, y = 10\sqrt{3}$

Step-by-step explanation:

In a 30°-60°-90° triangle, the shorter leg is represented by $\displaystyle x,$the longer leg is represented by $\displaystyle x\sqrt{3},$and the hypotenuse is represented by $\displaystyle 2x.$ So, evaluate:

$\displaystyle hypotenuse \hookleftarrow 2x \\ long\:leg \hookleftarrow x\sqrt{3} \\ short\:leg \hookleftarrow x \\ \\ 20\sqrt{3} = 2x\:[x\:is\:'y'\:in\:this\:case]; 10\sqrt{3} \\ \\ \\ x\sqrt{3} = x \\ \\ 30 = 10\sqrt{3}[\sqrt{3}]$

In the end, you arrive at this:

$\displaystyle x = 30, y = 10\sqrt{3}$

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