Question

find the volume of the oblique rectangular prism below. round your answer to the nearest tenth if necessary. 6 7 52° 15

Explanation:

Step1: Find the height of the prism

We know that in the right triangle formed, the hypotenuse is 15 and the angle is \(52^\circ\). Using the sine function \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\), the height \(h\) (opposite side to \(52^\circ\)) is \(h = 15\times\sin(52^\circ)\). Calculate \(\sin(52^\circ)\approx0.7880\), so \(h\approx15\times0.7880 = 11.82\).

Step2: Find the area of the base

The base is a rectangle with length 6 and width 7. The area of the base \(B=6\times7 = 42\).

Step3: Calculate the volume of the prism

The volume of a prism is given by \(V = B\times h\), where \(B\) is the area of the base and \(h\) is the height. Substituting the values, we get \(V=42\times11.82 = 496.44\approx496.4\) (rounded to the nearest tenth).

Answer:

\(496.4\)