Bell Ringer

1 / 12

# Bell Ringer - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Bell Ringer' - hea

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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.

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.

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.

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 .

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.

Now You Try 

3

3

3

10

Find Lengths in a Triangle

1.

14

2.

3.

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.

2.9 ≈ x

Use a calculator.

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

Example 5

The length of the shorter leg is 4.

The length of the longer leg is 4 .

3

Find Leg Lengths

Now You 

3

x = 21;y = 21 ≈ 36.4