Answer:
The height of the cone is 6.16 inches
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):
[tex]tan\text{ 72\degree = }\frac{opposite}{adjacent}[/tex][tex]\begin{gathered} tan\text{ 72\degree = }\frac{BC}{2} \\ BC\text{ = 2\lparen tan 72\degree \rparen} \\ BC\text{ = 2\lparen3.0777\rparen} \end{gathered}[/tex][tex]\begin{gathered} BC\text{ = 6.1554} \\ \\ The\text{ height of the cone is 6.16 in} \end{gathered}[/tex]
