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G-SRT.9 Warmup M3-044-A09-V02

Derive the triangle area formula A=1/2ab sin(C) using an auxiliary altitude.

Write a triangle area formula from two sides and the included angle

Problem

In the labeled triangle shown, sides \(a\) and \(c\) include angle \(B\). Write the triangle area formula using these measurements.

Standard triangle labeling with angle B between sides a and c, opposite side b, and an auxiliary altitude h. Open full size
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Four variants of this problem type
Curriculum context
Course
Math III
Standard
G-SRT.9
Category
Geometry
Domain
Similarity, Right Triangles, and Trigonometry
Objective
Derive the triangle area formula A=1/2ab sin(C) using an auxiliary altitude.
Problem type
Write a triangle area formula from two sides and the included angle