lilylac
Answered

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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! （╹◡╹）

Consider The 3060 Right Triangle Shown Whose Hypotenuse Is Equal To One Clearly This Triangle Is Half Of An Equilateral Triangle Please Help Me Thank You class=

Sagot :

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) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

cos(60°) = [tex]\frac{BC}{AC}[/tex]

BC = [tex]\frac{1}{2}(AC)[/tex]

BC = [tex]\frac{1}{2}[/tex]

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 + [tex](\frac{1}{2})^2[/tex]

1 = AB² + [tex]\frac{1}{4}[/tex]

AB = [tex]\sqrt{1-\frac{1}{4}}[/tex]

AB = [tex]\sqrt{\frac{3}{4}}[/tex]

AB = [tex]\frac{\sqrt{3} }{2}[/tex]

Length of the longer side = [tex]\frac{\sqrt{3}}{2}[/tex]

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