Problem preview
G-SRT.9 Warmup M3-044-A03-V01

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

Find the area of a triangle from two sides and the included angle

Problem

Find the area of the triangle shown with sides \(8\) and \(10\) and included angle \(30°\).

Big Picture

What this problem is really about

Treat one given side as the base and view the sine component of the other side as the perpendicular height. Substituting that height into one-half base times height produces the included-angle area formula. Match the angle specifically between the two supplied sides, and report the result in square units.

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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 the area of a triangle from two sides and the included angle