You have been hired to pour a concrete patio (i.e. your parents told you to do it correctly or be grounded for the rest of your life). they have requested that the patio be shaped as a right triangle with a depth of 8 inches. to save money, they have given you a measuring tape that is only 12 feet long which is the length of the shorter leg of the triangle. the shorter leg makes an 59o angle with the hypotenuse. to the nearest tenth of a cubic foot (ft^3), determine how much concrete you will need for the patio.

You want the volume in cubic feet of a right triangular prism that is 8 inches deep and has triangular faces with a short leg of 12 feet and an adjacent acute angle of 59°.

Long side

The long side of the right triangle can be figured using the tangent function:

Tan = Opposite/Adjacent

Opposite = Adjacent × Tan

long side = (12 ft)×tan(59°)

Area

The area of the right triangle is given by ...

A = 1/2bh

A = 1/2(12 ft)(12·tan(59°))

Volume

The volume of the prism is the product of its base area and its depth. There are 12 inches in a foot, so a depth of 8 inches is 8/12 of a foot.

V = Bh

V = (1/2·12·12·tan(59°))·(8/12) . . . . cubic feet

V ≈ 79.9 . . . . . cubic feet

You will need 79.9 cubic feet of concrete for the patio.

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Additional comment

We saved all the calculations until the end. No intermediate results are necessary. This way, the numbers are entered into the calculator only once.