Question

The axis of the cone 2m long makes an angle of 65 degrees with its horizontal base. What is the area of the base if its volume is 5 cu. m?

Answer 1

Guessing it looks like this...

Answer 2

but it is not a right triangle so i can't use SOH CAH TOA there

Answer 3

You still can. Notice the height h makes a right angle with the base.



Volume of a cone is 1/3x(area of base)x(height) or \[V = \frac{ 1 }{ 3 } B h\]
B is area of the base, h is height.

We can find height from the diagram: \[\sin 65 = \frac{ h }{2 }\]
so h=2sin65 and we know V = 5 cm^3
\[5 = \frac{ 1 }{ 3 } B \times 2 \sin 65\]