Answer:
9 feet
Step-by-step explanation:
Given:
A prism with a triangular base has a volume of 432 cubic feet.
The height of the prism is 8.
The triangle base has a base of 12 feet.
Question asked:
The height of the triangular base of the prism = ?
solution:
Volume of triangular prism = 
Dividing both side by 8
Multiplying both side by 2
Dividing both side by 12
Thus, height of the triangular base of the prism is 9
Answer:
- angle at A: 51°
- base angles: 64.5°
Step-by-step explanation:
The measure of the inscribed angle BAC is half the measure of the intercepted arc BC, so is 102°/2 = 51°.
The base angles at B and C are the complement of half this value, or ...
90° -(51°/2) = 64.5°
The angle measures in the triangle are ...
∠A = 51°
∠B = ∠C = 64.5°
We need to solve for the radius
circumference = radius * 2 * PI
radius = circumference / (2*PI)
radius = 4.5 / (
<span>
<span>
<span>
6.2831853072
</span>
</span>
</span>
)
radius =
<span>
<span>
<span>
0.7161972439
</span>
</span>
</span>
feet
Formula for cylinder volume:
<span>Volume = </span><span>π • r² • height</span>
Volume = <span>π • (</span><span>
<span>
<span>
0.7161972439)^2 * 12
</span></span></span>Volume = PI * <span><span>0.5129384922
</span>
* 12
Volume </span><span><span><span>19.3373255857
</span>
cubic feet
</span> </span>
