The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle? 5 StartRoot 2 EndRoot units 4 StartRoot 3 EndRoot units 10 StartRoot 2 EndRoot units 16 StartRoot 5 EndRoot units

The altitude is 4√3 units long

Step-by-step explanation:

Since the triangle is equilateral, all the sides will measure 8 units.

Now to find the altitude, we drop a line from the middle vertex to the horizontal line below and this splits the horizontal line into 2 equal parts which measures 4 units exactly.

Now we will be having 2 right-angled triangles, with the hypotenuse of each measuring 8 units and the other side measuring 4 units

Mathematically to find the altitude, we can solve using Pythagoras’ theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides

Let’s call the altitude h;

8^2 = h^2 + 4^2

64 = h^2 + 16

h^2 = 64-16

h^2 = 48

h= √(48)

h = 4 √3 units

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

answer: c. is your answer

step-by-step explanation: get me a black leather coat