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

Answer:

Step-by-step 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°) = $\frac{BC}{AC}$

BC = $\frac{1}{2}(AC)$

BC = $\frac{1}{2}$

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 + $(\frac{1}{2})^2$

1 = AB² + $\frac{1}{4}$

AB = $\sqrt{1-\frac{1}{4}}$

AB = $\sqrt{\frac{3}{4}}$

AB = $\frac{\sqrt{3} }{2}$

Length of the longer side = $\frac{\sqrt{3}}{2}$