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Chapter 5: Problem 60

A parking lot has the shape of a parallelogram (see figure). The lengths of two adjacent sides are 70 meters and 100 meters. The angle between the two sides is \(70^{\circ} .\) What is the area of the parking lot?

Short Answer

Expert verified
To calculate the area of the parallelogram-shaped parking lot, we can use the provided measurements of the sides and the included angle, applying the formula \(A = a \times b \times \sin(C)\), and converting the angle to radians for the calculation. After plugging in the measurements and carrying out the computation, we get the area of the parking lot.

Step by step solution

01

Identify the given parameters.

The length of two adjacent sides of the parallelogram (the parking lot) are \(70 m\) and \(100 m\). The angle between them is \(70^{\circ}\).
02

Apply the formula for the area of a parallelogram.

Apply the formula \(A = a \times b \times \sin(C)\), where \(a\) and \(b\) are lengths of the two sides, and \(C\) is the angle in between. In this case, \(a = 70 m\), \(b = 100 m\), and \(C = 70^{\circ}\). Before the multiplication, make sure to convert the angle from degrees to radians because the \(\sin\) function in calculations uses radians.
03

Compute the area of the parallelogram.

Firstly, convert \(70^{\circ}\) to radians: \(70^{\circ} = 70 \times \pi / 180\) rad. Now, substitute the values into the formula for the area of a parallelogram: \(A = 70 \times 100 \times \sin(70 \times \pi / 180)\). Solving the calculation will provide the area of the parking lot in square meters.

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