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G-SRT.8.1 Warmup M2-054-A09-V02

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

Apply the correct special right-triangle family in context

Problem

An equilateral sign has side length \(10~\text{in}\). Its altitude forms a \(30-60-90~\text{triangle}\) with short leg \(5~\text{in}\) and hypotenuse \(10~\text{in}\). Use the special-triangle ratio to calculate the altitude exactly.

Prompt equilateral-sign diagram with side length 10 inches and an altitude drawn to the base. The altitude splits the base in half; its length is unknown and withheld. 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
Apply the correct special right-triangle family in context