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

Find The Height Of The Cone Round To The Nearest Hundredth If Necessary Show Your Work class=

Sagot :

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]

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