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G-SRT.8.1 Warmup M2-054-A10-V04

Derive and use trig ratios for 30-60-90 and 45-45-90 special right triangles.

Choose whether to use a 45-45-90 triangle or a 30-60-90 triangle

Problem

A diagonal cuts a square into \(\text{two}~\text{right}~\text{triangles}\) with equal legs. Use the isosceles-right-triangle angle relationship to determine \(\text{both}~\text{acute}~\text{angles}\), then name the special-right-triangle family.

Unworked special-triangle or construction diagram showing only supplied measures and requested unknowns. Open full size
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-SRT.8.1
Category
Geometry
Domain
Similarity, Right Triangles, and Trigonometry
Objective
Derive and use trig ratios for 30-60-90 and 45-45-90 special right triangles.
Problem type
Choose whether to use a 45-45-90 triangle or a 30-60-90 triangle