Question

if the area of \\( \triangle a b c \\) is \\( d \\), give the expressions that complete the equation for the measure of \\( \angle c \\).
\\( m \angle c = \sin ^ { - 1 } \left( \frac { m } { n } \
ight) \\)
\\( m = \\)
\\( n = \\)

Explanation:

Step1: Recall the formula for the area of a triangle

The area formula for a triangle is \(D=\frac{1}{2}ab\sin C\).

Step2: Solve the formula for \(\sin C\)

Multiply both sides of \(D = \frac{1}{2}ab\sin C\) by \(2\) to get \(2D=ab\sin C\). Then divide both sides by \(ab\) to obtain \(\sin C=\frac{2D}{ab}\).

Answer:

\(m = 2D\), \(n=ab\)