Chapter MPS, Problem 14.1MPS

To determine

Rewrite the formula in terms of $\csc C$ .

Answer to Problem 14.1MPS

  $\frac{ab}{2\csc C}$

Explanation of Solution

Given information:

The area of the triangle can be determined by the formula $A=\frac{1}{2}ab\sin C.$

  

Calculation:

Consider the formula:

  $A=\frac{1}{2}ab\sin C.$

Recollect the reciprocal identity:

  $\sin C=\frac{1}{\csc C},\csc C\ne 0$

Use the above reciprocal identity, rewrite the formula,

  $\begin{array}{l}A=\frac{1}{2}ab\sin C\\ =\frac{1}{2}ab.\frac{1}{\csc C}\\ =\frac{ab}{2\csc C}\end{array}$