To show: The area of triangle is
Explanation of Solution
Given information:
The three angles of triangle are A, B and C and one side is a .
Formula used:
The area of a triangle is denoted by
The sine rule for a triangle is
Proof:
It is provided that three angles of triangle are A, B and C and one side is a .
Construct a triangle with given conditions. Also label the side opposite to angle B as b and opposite to angle C as c .
Recall that the sine rule for a triangle is
From the above expression, from the figure sketched above it is clear that
Now, observe in the figure that the included angle between the sides a and b is C .
Recall that he area of a triangle is denoted by
Therefore,
Hence, it is shown that the area of triangle is
Chapter 6 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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