Question

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Answer 1

Option A.

Explanation:

A 30° - 60° - 90° triangle is a Right Triangle that has special side measures.

Let's summarize the sides in a ratio.

`Short \ Leg: Long \ Leg: Hypotenuse\\x:x √(3) : 2x`

The short leg is just x.

The long leg is multiplied by
`√(3)`.

The hypotenuse is double of the short leg.

For example, if the short leg is 2;

`Short \ Leg = 2\\Long \ Leg = 2√(3) \\Hypotenuse = 4`

Let's look at the 4 options provided. We should check if the values of the sides match with a 30° - 60° - 90° triangle.

Option A has a short leg with the value of 5.

The long leg is correct, it's multiplied by
`√(3)`.

The hypotenuse is correct, it's double of the short leg.

Option A is correct!

Option B has a short leg with the value of 5.

The long leg is correct, it's multiplied by
`√(3)`.

The hypotenuse is incorrect, it's triple of the short leg.

Option B is incorrect.

Option C has a short leg with the value of 5.

The long leg is incorrect, it's multiplied by
`2√(3)`.

The hypotenuse is correct, it's double of the short leg.

Option C is incorrect.

Option D has a short leg with the value of 10.

The long leg is incorrect, it's multiplied by
`(1)/(2) √(3)`.

The hypotenuse is incorrect, it's
`1 (1)/(2)` of the short leg.

Option D is incorrect.

Our only 30° - 60° - 90° triangle is Option A.