Lesson 2: 8-3 Special Right Triangles

1. Given the length of one side of a triangle with angle measures 45, 45, and 90 degrees, how do we find the other two sides?
1. Given the length of one side of a triangle with angle measures 30, 60, and 90 degrees, how do we find the other two sides?

G.SRT.6
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

A 45-45-90 triangle is the only type of isosceles right triangle. The hypotenuse is the (square root of 2) times the length of the leg. A 30-60-90 triangle also has special properties. The measures of the sides are x (shortest side), x times (square root of 3) (middle length side), and x times 2 (longest side). Knowing these properties can save valuable time when you are solving problems involving special right triangles.

As part of a packet for students attending a regional student council meeting, Lyndsay orders triangular highlighters. She wants to buy rectangular boxes for the highlighters and other items, but she is concerned that the highlighters will not fit in the box she has chosen. If she knows the length of the side of the highlighter, Lyndsay can use the propterties of special right triangles to determine if it will fit in the box.

When giving final answers that involve radicals, students should be sure to rationalize all denominators. Fractions should not have radicals in the denominator.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher.
Students beyond grade level can make deeper connections by solving more complicated real world problems involving special right triangles.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.