Bell Ringer What are special right triangles?

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Presentation transcript:

Bell Ringer 12-7-17 1. What are special right triangles? 2. What are the rules for a 45-45-90 triangle? 3. What are the rules for a 30-60-90 triangle?

Special Right Triangles (review from Math II) Thursday, December 7, 2017

Special right triangles 45-45-90 and 30-60-90 are Special Right Triangles. A 45-45-90 triangle has angles in a 1-1-2 ratio. A 30-60-90 triangle has angles in a 1-2-3 ratio. Because of these angle ratios, the sides have special rules…. See information in chapter 9.4 in the Geometry book (p. 551-553).

45-45-90 Leg = x Hypotenuse = x√2 A 45-45-90 triangle is also called an Isosceles Right Triangle. This triangle has a hypotenuse and congruent legs. The hypotenuse is the leg times the square root of 2. Leg = x Hypotenuse = x√2

30-60-90 Short Leg = x Long Leg = x√3 Hypotenuse = 2x This triangle has a hypotenuse, a long leg, and a short leg. We know the longest sides of a triangle are across from the biggest angle and the shortest are across from the smallest angle, so the short leg is across from the 30° angle and the long leg is across from the 60° angle. Short Leg = x Long Leg = x√3 Hypotenuse = 2x

examples The rule is the hypotenuse is the leg times the square root of 2, so x = 8√2. The rule is the hypotenuse is twice the short leg, so y = 16. The rule is the long leg is the short leg times the square root of 3, so x = 8√3.

Assignments Classwork: Geometry book p.554-555 #12-29 all Homework: Trigonometry Prerequisite: Special Right Triangles

Exit Ticket 1. Which special right triangle is also known as an isosceles right triangle? 2. In a 30-60-90, how does the short leg relate to the long leg? 3. In a 45-45-90, how do the legs relate to the hypotenuse?