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Overview
Precalculus
14. CC.HSG.SRT.D.9
14.1 Area of triangles: 1/2 a*b sin(C)
Area of a Triangle Using Sine: the 1/2 ab sin C Formula
Find the area of any triangle when you know two sides and the angle between them, using the formula Area equals one half a b sin C.
What You'll Learn
Identify the two known sides and the included angle before applying \( A = \frac{1}{2}ab\sin(C) \).
Derive the formula by treating a sin C as the triangle's height relative to base b
Calculate the area directly when two sides and the angle between them are given, with no need to find the height first
Substitute known values carefully, making sure the angle used is always the one between the two given sides
Rearrange the formula to solve for a missing side or angle when the area is already known
Recognize when to switch to the law of cosines or sine law for problems that ask for a side or angle instead of area
This Unit Includes
7 Video lessons
Learning resources
IL Curriculum Aligned