Problem preview
G-SRT.8.1 Warmup M2-054-A02-V01

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

Use the symbolic1:√3:2 relationship in a30-60-90 triangle

Problem

A \(30-60-90\) triangle has short leg \(s\). Apply the \(1:\sqrt{3}:2\) ratio to express the short leg, long leg, and hypotenuse in order.

Big Picture

What this problem is really about

The thirty-sixty-ninety ratio is ordered by the sides opposite thirty, sixty, and ninety degrees. We’ll map those to short leg, long leg, and hypotenuse, scale the one-to-square-root-of-three-to-two pattern by the symbolic short leg, and verify the three expressions with the Pythagorean theorem.

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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
Use the symbolic1:√3:2 relationship in a30-60-90 triangle