Answer:
√3/2 or 0.866
Step-by-step explanation:
Use special triangles. (See attachment)
The cosine ratio is adjacent ÷ hypotenuse.
cos30° = √3 ÷ 2 = √3/2
As a decimal, cos30° ≈ 0.866
Remember all the primary trig ratios with the acronym SohCahToa.
"o" = opposite
"a" = adjacent
"h" = hypotenuse
S, C and T are sin, cos, tan
we know that
The volume of the prism is equal to
where
B is the area of the base
h is the height of the prism
Step 1
<u>Find the area of the rectangular base</u>
we know that
the area of a rectangle is equal to
In this problem we have
Step 2
<u>Find the height of the prism</u>
Applying the Pythagoras Theorem
solve for h
Step 3
<u>Find the volume of the prism</u>
The volume of the prism is equal to
substitute the values
therefore
<u>the answer is</u>