Problem preview
G-SRT.8.1 Warmup M2-054-A03-V01

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

Find missing side lengths in a 45-45-90 triangle using \(x, x, x sqrt(2)\)

Problem

In a \(45-45-90\) triangle, \(\text{one}~\text{leg}\) is \(9\). Find the missing side lengths.

Big Picture

What this problem is really about

Equal acute angles make the two legs equal, while the radical factor belongs only to the hypotenuse. We’ll transfer the known leg length to the other leg, scale it by square root of two for the hypotenuse, and check both sides of the Pythagorean equation.

Inside Gozunta

Turn the preview into practice.

More than a preview

Gozunta lets you study this problem—and more than 10,000 others.

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now
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
Find missing side lengths in a 45-45-90 triangle using \(x, x, x sqrt(2)\)