Question

Special right triangle

Answer 1

Problem 1

Answers:

a = 6

b =
`6√(3)`

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Reason:

The short leg is opposite the smallest angle. For any 30-60-90 triangle, the short leg is half the hypotenuse. This means the short leg is 12/2 = 6 units long. That's why a = 6.

The long leg is
`√(3)` times longer compared to the short leg.

`\text{long leg} = (\text{short leg})*√(3)\\\\\text{long leg} = 6√(3)`

This template applies to 30-60-90 triangles only.

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Problem 2

Answer:

a = 7

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Reason:

We use the same idea mentioned in problem 1. The short leg is half as long as the hypotenuse. It works for 30-60-90 triangles only.