Question

To the nearest hundredth of a centimeter, what is the length of the hypotenuse?

Answer 1

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`\text {Use sin x = } (opp)/(hyp)`
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`sin (30) = (53.57)/(y)`


`y = (53.57)/(sin (30))`


`y = 107.14 \ cm`

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Answer: 107.14 cm
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Answer 2

We see that this right triangle has a 30°-angle, meaning the remaining angle must be 60° (sum of angles must be 180°). This means the triangle is what we call a special right triangle, specifically, a 30°-60°-90° triangle.

The sides of such a triangle are in a ratio where the shortest leg (across from the 30°-angle) is x, the hypotenuse is 2x, and the longest leg is x√3.

Here, we are given the shortest leg, 53.57 cm. To get the hypotenuse, we double this length to get 107.14 cm.