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Chapter 5: Problem 40

Find the area of the triangle having the indicated angle and sides. $$B=130^{\circ}, \quad a=62, \quad c=20$$

Short Answer

Expert verified
The area of the triangle is approximately 602.88 square units.

Step by step solution

01

Identify the known values

From the exercise, we clearly understand that the angle B is \(130^{\circ}\), side a is 62 units and side c is 20 units.
02

Convert the angle from degrees to radians

Since Python calculates the sine of an angle in radians, we must first convert the angle from degrees to radians. You can perform the conversion using the formula: radians = degrees * \( \pi / 180 \). Thus, the angle B in radians is \((130 * \pi) / 180\).
03

Substitute the values into the area formula

The formula for the area of a triangle when two sides and the included angle are known is \(0.5*a*c*sin(B)\). So, the area of the triangle is \(0.5*62*20*sin((130 * \pi) / 180)\).
04

Calculate the area

Once you have substituted all values into the formula, you can now calculate the area.

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