1 / 12

Bell Ringer

Bell Ringer. 30-60-90 Triangles. A Right Triangle with angle measures of 30, 60, and 90 are called 30-60-90 triangles. Example 1. In the diagram,  PQR is a 30 ° – 60 ° – 90 ° triangle with PQ = 2 and PR = 1 . Find the value of b. 3. b =. Take the square root of each side.

hea
Download Presentation

Bell Ringer

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bell Ringer

  2. 30-60-90 Triangles • A Right Triangle with angle measures of 30, 60, and 90 are called 30-60-90 triangles.

  3. Example 1 In the diagram, PQR is a 30°–60°–90°triangle with PQ = 2 and PR = 1. Find the value of b. 3 b = Take the square root of each side. Find Leg Length SOLUTION You can use the Pythagorean Theorem to find the value of b. (leg)2 + (leg)2 = (hypotenuse)2 Write the Pythagorean Theorem. 12 + b2 = 22 Substitute. 1 + b2 = 4 Simplify. b2 = 3 Subtract 1 from each side.

  4. Example 2 Find Hypotenuse Length In the 30°–60°–90° triangle at the right, the length of the shorter leg is given. Find the length of the hypotenuse. SOLUTION The hypotenuse of a 30° –60° –90° triangle is twice as long as the shorter leg. hypotenuse = 2 · shorter leg 30° –60° –90° Triangle Theorem = 2 · 12 Substitute. = 24 Simplify. The length of the hypotenuse is 24. ANSWER

  5. Example 3 SOLUTION The length of the longer leg of a 30° –60° –90° triangle is the length of the shorter leg times . longer leg = shorter leg · 30° –60°–90° Triangle Theorem = 5 · Substitute. 3 3 3 3 The length of the longer leg is 5 . ANSWER Find Longer Leg Length In the 30°–60°–90° triangle at the right, the length of the shorter leg is given. Find the length of the longer leg.

  6. Now You Try  3 ANSWER 3 3 10 ANSWER Find Lengths in a Triangle Find the value of x. Write your answer in radical form. 1. 14 ANSWER 2. 3.

  7. Example 4 In the 30°–60°–90° triangle at the right, the length of the longer leg is given. Find the length x of the shorter leg. Round your answer to the nearest tenth. SOLUTION The length of the longer leg of a 30° –60° –90° triangle is the length of the shorter leg times . longer leg = shorter leg · 30°–60°–90° Triangle Theorem 5 = x· Substitute. 3 3 3 3 5 = x Divide each side by . 3 Find Shorter Leg Length The length of the shorter leg is about 2.9. ANSWER 2.9 ≈ x Use a calculator.

  8. Example 5 In the 30°–60°–90° triangle at the right, the length of the hypotenuse is given. Find the length x of the shorter leg and the length y of the longer leg. Shorter leg Longer leg 3 3 3 longer leg = shorter leg · hypotenuse = 2 · shorter leg y = 4 · y = 4 Find Leg Lengths SOLUTION Use the 30° –60° –90° Triangle Theorem to find the length of the shorter leg. Then use that value to find the length of the longer leg. 8 = 2 ·x 4 = x

  9. Example 5 The length of the shorter leg is 4. ANSWER The length of the longer leg is 4 . 3 Find Leg Lengths

  10. Now You  3 x = 21;y = 21 ≈ 36.4 ANSWER Find Leg Lengths Find the value of each variable. Round your answer to the nearest tenth. 4. 3.5 ANSWER 5.

  11. Page 552

  12. Page 552 #s 2-36 even only

More Related