Question

A company logo is shaped like an equilateral triangle with 2-in.-long sides. What is the height of the logo? Round to the nearest tenth. A. 1.0 in. B. 1.7 in. C. 2.0 in. D. 1.4 in.

Answer 1

Answer:

B. 1.7 in

Step-by-step explanation:

Divide the triangle into 2 congruent right angle triangles

With hypotenuse: 2

Base: 2/2 = 1

Using pythagoras theorem

2² = 1² + h²

h² = 3

h = sqrt(3)

h = 1.732050808

Answer 2

The height of the equilateral triangle is required.

The height of the logo is option B. 1.7 in.

A perpendicular to from one of the vertices of an equilateral triangle bisects the sides into two equal halves.

a = Length of every side of the equilateral triangle = 2 in

b = Length of the bisected length = $\dfrac{2}{2}=1\ \text{in}$

From the Pythagoras theorem we have

$a^2=h^2+b^2\\\Rightarrow h=\sqrt{a^2-b^2}\\\Rightarrow h=\sqrt{2^2-1^2}\\\Rightarrow h=1.7\ \text{in}$

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