Question

Consider the 30°-60° right triangle shown whose hypotenuse is equal to one. Clearly this triangle is half of an equilateral triangle. Please help me. Thank you! （╹◡╹）

Answer 1

Explanation:

Given triangle ABC is a right triangle.

m∠ACB = 60°

m∠CAB = 30°

m(AC) = 1 unit

A). Shorter side of the given triangle = Side BC

By applying cosine rule,

cos(∠C) =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

cos(60°) =
`(BC)/(AC)`

BC =
`(1)/(2)(AC)`

BC =
`(1)/(2)`

Length of the shorter side = 0.5 units

B). Longer side of the given triangle = side AB

By applying Pythagoras theorem in the given triangle,

AC² = AB² + BC²

1² = AB² +
`((1)/(2))^2`

1 = AB² +
`(1)/(4)`

AB =
`\sqrt{1-(1)/(4)}`

AB =
`\sqrt{(3)/(4)}`

AB =
`(√(3) )/(2)`

Length of the longer side =
`(√(3))/(2)`