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padilas [110]
3 years ago
15

The hypotenuse of a 30o-60o-90o triangle measures 4 square 3 inches. What is the length of the shorter leg?

Mathematics
1 answer:
Fofino [41]3 years ago
5 0

<u><em>Answer:</em></u>

The shorter leg is 2\sqrt{3} inches

<u><em>Explanation:</em></u>

The 30°-60°-90° is a special type of right-angled triangles

<u>It has the following special side length:</u>

The length of the side opposite to the 30° is \frac{1}{2} the length of the hypotenuse

The length of the side opposite to the 60° is \frac{\sqrt{3} }{2} of the hypotenuse

<u>Now, we know that</u> the lengths of the sides in a triangle are proportional to the angles

<u>This means that</u> the shortest side will be the one opposite to the smallest angles

In our case, the shortest side will be the one opposite to the 30° angle

We are given that the hypotenuse of the triangle is 4\sqrt{3} in

<u>From the above:</u>

Shorter leg = leg opposite to 30° = \frac{1}{2} * hypotenuse = \frac{1}{2} * 4\sqrt{3} = 2\sqrt{2} inches

Hope this helps :)

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