Question

Find the height of the cone. Round to the nearest hundredth, if necessary. Show your work.

Answer 1

Answer:

The height of the cone is 6.16 inches

Step-by-step explanation:

Given:

diameter of the cone = 4 inches

Angle BAC = 72°

To find:

the height of the cone

To determine the height of the cone, we will use the right-angled triangle formed in the cone:

Diameter = 2(radius)

radius = diameter/2

radius = 4/2

radius = 2 inches

Height = BC

To get the height, we will apply the tan ratio (TOA):

`tan\text{ 72\degree = }(opposite)/(adjacent)`
`\begin{gathered} tan\text{ 72\degree = }(BC)/(2) \\ BC\text{ = 2\lparen tan 72\degree \rparen} \\ BC\text{ = 2\lparen3.0777\rparen} \end{gathered}`
`\begin{gathered} BC\text{ = 6.1554} \\ \\ The\text{ height of the cone is 6.16 in} \end{gathered}`