Question

Find the value of the variables. if the answer is not an integer, express it in simplest form ​

Answer 1

A. x = (20√3)/3, y = (40√3)/3

Explanation:

The ratios of the side lengths of a 30°-60°-90° right triangle are (shortest to longest) ...

1 : √3 : 2

In this triangle, they are ...

x : 20 : y

Multiplying the first ratio by (20√3)/3, we get ...

x : 20 : y = (20√3)/3 : 20 : (40√3)/3

Then the values of the variables are x = (20√3)/3, y = (40√3)/3.

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The above side length ratios correspond to sin(60°) = cos(30°) = (√3)/2, cos(60°) = sin(30°) = 1/2. These are values you might have memorized.