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Chapter 6: Problem 67

How is the sine function used to find the area of an oblique triangle?

Short Answer

Expert verified
The sine function is used in the formula \( \frac{1}{2} a b \sin(C) \) to compute the area of an oblique triangle. This formula needs the lengths of any two sides of the triangle ('a' and 'b') and the angle ('C') between them. Perform the calculations and the result is the triangle's area.

Step by step solution

01

Observation

First, assess if you are dealing with an oblique triangle. Ensure you have the length of two sides and the size of the angle between these two sides.
02

Apply Formula

Next, apply the formula for the area of an oblique triangle. This formula is \( \frac{1}{2} a b \sin(C) \), wherein 'a' and 'b' are the lengths of the sides of the triangle and 'C' is their included angle.
03

Calculation

Proceed to input the values of the lengths of the sides and the angle into the formula and carry out the calculations. If the angle is not provided in radians, consider converting to radians before calculation as the sine function in most calculators assumes the angle is in radians.
04

Result

The number you arrive at after your calculations is the area of the oblique triangle.

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