Question

Using the technique in the model above, find the missing sides in this 30°-60°-90° right triangle. the short leg =2

Answer 1

Hypotenuse is 4 and the long leg is 2√3

Explanation:

To find the hypotenuse simply multiply the length of the short leg by 2. so 2·2= 4. Therefore, the hypotenuse is equal to 4.

For the long leg you multiply the short leg by √3. So 2·√3 = 2√3.

So in conclusion,

Hypotenuse= 4

Long leg= 2√3

Answer 2

This is the special right angle triangle 30°-60°-90° as shown below in the figure.

• The side opposite the 30° angle is always the shortest because 30 degrees is the smallest angle.

• The side opposite the 60° angle will be the longer side, because 60 degrees is the mid-sized degree angle in this triangle.

• Finally , the side opposite the 90° angle will always be the largest side(Hypotenuse) because 90 degrees is the largest angle.

In 30°−60°−90° right triangle,

• the length of the hypotenuse is twice the length of the shorter side,

• also, the length of the longer side is
  `√(3)` times the length of the shorter leg.

Given: length of short(S) = 2 units

To find the missing side, i.e hypotenuse(H) and longer side(L);

Then,

length of longer sides(L) =
`√(3) * S`

Substitute the value of S = 2 we get;

`L = √(3) * 2 = 2√(3)` units.

Length of hypotenuse(H) =
`2 * S`

Substitute the value of S = 2 we get;

`H=2 * 2 = 4` units.

therefore, the missing sides are:

Hypotenuse(H) = 4 units and

Longer side(L) =
`2√(3)` units.