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.

draw a vertical and you will have right-angled triangle with sides 1, h, and hypotenuse of 2

solve for h
h^2 + 1^2 = 2^2

Not not know

To find the height of the equilateral triangle logo, we can use the properties of an equilateral triangle.

The height of an equilateral triangle is the line segment from one vertex perpendicular to the base. In this case, the side length of the equilateral triangle (s) is given as 2 inches.

To find the height, we can construct an altitude from one vertex to the midpoint of the opposite side. This will divide the equilateral triangle into two congruent right triangles.

In a right triangle, the length of the hypotenuse is twice the length of a leg. Therefore, the length of the altitude (h) is half the length of the side.

Using the formula for the area of an equilateral triangle, we have:

Area = (sqrt(3)/4) * s^2

Substituting the given value for the side length:

Area = (sqrt(3)/4) * (2^2)
Area = (sqrt(3)/4) * 4
Area = sqrt(3)

We know that the area of the equilateral triangle is equal to (base * height) / 2. In this case, the base is the side length of the triangle, which is 2 inches, and the height is the length of the altitude that we are trying to find. So we have:

(sqrt(3)) = (2 * h) / 2
sqrt(3) = h

Therefore, the height of the logo is √3 inches. Rounding to the nearest tenth, the height is approximately 1.7 inches.

h^2+1^2=2^2

h^2+1=4
-1 -1
h^2= 3 Take out the square root of h^2 and 3
and the answer is: h= squareroot of 3