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Chapter 6: Problem 72

Determine whether each statement makes sense or does not make sense, and explain your reasoning. If I know the measures of the sides and angles of an oblique triangle, I have three ways of determining the triangle's area.

Short Answer

Expert verified
The statement does not make sense, as there are primarily two methods for determining the area of an oblique triangle when we know the measures of its sides and angles: Heron's formula and the Sine rule.

Step by step solution

01

Understanding the statement

An oblique triangle is simply any triangle that is not a right triangle. It can either be an acute triangle (all angles less than 90 degrees) or an obtuse triangle (one angle greater than 90 degrees). The given statement mentions that if the measures of the sides and angles of an oblique triangle are known, then there are three ways of determining the triangle's area.
02

Identifying possible ways to determine the area

Typically, the most common way to determine the triangle's area is using the Heron's formula that only requires the length of sides. Another way could be using the formula, \[ \frac{1}{2}ab \sin C \] which uses two sides and included angle. We see already two methods to find the area, but is there a third method?
03

Analyzing the possibility of a third method

There appears not to be a standard third formula for finding the area of an oblique triangle. Though other methods may exist, they are either variations or combinations of the two mentioned formulas, or require additional constraints. Hence, the statement does not make sense.

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