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G-SRT.9 Warmup M3-044-A04-V02

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

Find a missing side using the triangle area formula A = (1/2)ab sin(C)

Problem

The triangle shown has area \(24\), side \(b~=~8\), and included angle \(A~=~60°\). Use the triangle area formula to find \(c\) exactly.

Prompt triangle with area 24, side b=8, included angle A=60°, and side c unknown. 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
Find a missing side using the triangle area formula A = (1/2)ab sin(C)