Download presentation

Presentation is loading. Please wait.

Published byJune Patrick Modified over 6 years ago

1
Warmup:Solve for y

2
8.2 Special Right Triangles LEQ: What are special right triangles and how do we use them?

3
The “root” of it all… Calculate the value of each hypotenuse in a triangle as a reduced radical… Do you notice a trend? Is there an easier way to calculate (shortcuts)? (hint: label sides with numbers)

4
Side lengths of Special Right Triangles Right triangles whose angle measures are 45°-45°-90° or 30°- 60°-90° are called special right triangles. The theorems that describe these relationships of side lengths of each of these special right triangles follow….

5
Theorem 8-5: 45°-45°-90° Triangle Theorem In a 45°-45°-90° triangle, the hypotenuse is √2 times as long as each leg. x√2 45 ° Hypotenuse = leg ∙ √2

6
Finding the hypotenuse in a 45°- 45°-90° Triangle Ex 1: Find the value of x at the right. Ex 2: Find the length of the hypotenuse of a 45- 45-90 triangle with legs of length 5√3. 2√16 x 45 °

7
Finding a leg in a 45°-45°-90° Triangle Ex. 3 Find the value of x and y. 5 x y 45 °

8
Theorem 8-6: 30°-60°-90° Triangle Theorem In a 30°-60°-90° triangle: –the hypotenuse is twice as long as the shorter leg –the longer leg is √3 times as long as the shorter leg. x√3 60 ° 30 ° Hypotenuse = 2 ∙ (shorter leg) Longer leg = (shorter leg) ∙ √3

9
Alternatives? OF COURSE!! If you don’t care for shortcuts, you may memorize… 1 1 √2 1 2 √3 30 60 45

10
Finding side lengths in a 30°-60°- 90° Triangle Ex. 1 Find the values of s and t and the right. Ex. 2 Find the value of each variable. 30 ° 60 ° 30 ° 60 ° 8 x y

11
Real World Connection The yield sign is an equilateral triangle. It has a height of 18√3. Find x and y. 18√3 y inch. x inch.

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google