Geometry, Teacher\'s Edition

Solution:

To solve this problem, you can use the Pythagorean Theorem since each of the bases is at a 90◦angle.

Therefore, you can split up the baseball diamond into 45− 45 −90 triangles.

90^2 + 902 =c^2

8100+ 8100 =c^2

16200=c^2

127.2 feet is the distance from first to third base.

III.TechnologyIntegration

Have the students complete a websearch on baseball fields across the United States.

Students can select their favorite one and report on its dimensions.

Does the Pythagorean Theorem work for all baseball diamonds?

Conduct a discussion exploring the angles and dimensions of baseball diamonds.

IV.NotesonAssessment

Were the students able to solve the problem?

Were there struggles?

Did the students see the right angles in the diamond?

Did they notice that they could divide the diamond into two 45− 45 −90 triangles?

Where is the hypotenuse of the triangles?

Assess student work and provide feedback as needed.

Tangent Ratios

I.SectionObjectives

Identify the different parts of right triangles.

Identify and use the tangent ratio in a right triangle.

Identify complementary angles in right triangles.

Understand tangent ratios in special right triangles.

II.Cross-curricular-Art/FurnitureMaking

Have the students look at the website or show them the images of the triangle table.

You can use this as a discussion piece.

Ask the students to identify the parts of the right triangle.

Then ask them to identify the tangent ratio of the right triangle.

Finally, students can be given the task of constructing their own right triangle table.

Students will need tools and saws to do this.

You may want to see if you can combine this activity with woodshop, if offered in your school.

Have the students share their work when finished.

III.TechnologyIntegration

Have the students explore the concept of dragon tiles that have right angles in them.

The students can go to the following website to explore this.

3.8. Right Triangle Trigonometry