Question

Using the triangle theorem solve this triangle.​

Answer 1

Explanation:

30-60-90 triangle is a special right triangle whose angles are 30º, 60º, and 90º. The triangle is special because its side lengths are always in the ratio of 1: √3:2.

Answer 2

a = 2
`√(3)` , c = 4
`√(3)`

Explanation:

Using the tangent ratio in the right triangle and the exact value

tan30° =
`(√(3) )/(3)` , then

tan30° =
`(opposite)/(adjacent)` =
`(a)/(b)` =
`(a)/(6)` =
`(√(3) )/(3)` ( cross- multiply )

3a = 6
`√(3)` ( divide both sides by 3 )

a = 2
`√(3)`

Using Pythagoras' identity in the right triangle

c² = 6² + (2
`√(3)` )² = 36 + 12 = 48 ( take square root of both sides )

c =
`√(48)` =
`√(16(3))` = 4
`√(3)`