The three pairs are (AB = 6, BC = 6) (AB = 4, AC = 4√2) and (BC = 2√2, AC = 4). So, First option, Option 5. and Option 6 are correct answers.
What is trigonometry?
Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
The formula for a 30-60-90 triangle is this:
1) Side opposite to 30 will be value a.
2) Side opposite to 60 will be value a√3
3) Hypotenuse will be 2a.
AB is opposite of the angle with 30 degree measurement.
BC is opposite of the angle with 60 degree measurement.
The sides of an isosceles right triangle are in the ratio,
1:1:√2
where √2 is the hypotenuse.
For the example, BC = 2√2, then AC = 2√2 x √2 = 4.
Therefore, the three pairs are;
1. (AB = 6, BC = 6)
5. (AB = 4, AC = 4√2)
6.(BC = 2√2, AC = 4).
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