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hodyreva [135]
3 years ago
6

Consider the 30°-60° right triangle shown whose hypotenuse is equal to one. Clearly this triangle is half of an equilateral tria

ngle. Please help me. Thank you! (╹◡╹)

Mathematics
1 answer:
Bad White [126]3 years ago
3 0

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}

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