Airplane Take-Off

Ask students:

"What information do you need to solve the problem?"

"How will your information allow you to solve the problem?"

But only give them the following information:

Allow students to engage in productive struggle. Some students may be able to solve using similar triangles (perhaps they will ask for a protractor, or use the image above and a ruler if you provide them to students).

Otherwise, it's likely students will get stuck. Stop the class and explain that we need to develop some new math concepts to solve this problem. Then introduce the following investigation:

Right Triangle Investigation

1. Use a protractor to construct 3 right triangles of different sizes that contain a 30 degree angle. Label the right angle and the 30 degree angle.

2. Measure the side lengths of each triangle and record in the table below.

3. For each triangle, divide the opposite side measurement by the adjacent side measurement. Record in the third column in the table.

4. What do you notice/observe?

5. Compare your work with the work of your classmates. What do you notice/observe?

6. Would your observation be true for angles other than 30 degrees in a right triangle? Test it out!

Students should observe that, given a specific angle in a right triangle of any size, the ratio between the opposite side and adjacent side to the angle is the same. Have students discuss or complete a reflection activity (See the lesson files for a possible activity).

Have students complete the airplane task.

Possible Extension Questions:

• If the mountain were 3000 feet tall, by how many degrees would the plane have to adjust?
• At what height would the mountain be too tall for the plane to overcome with adjustments?
• How long will it take for the plane to reach the mountain? What information would you need to know? Where could you find that information, or how could you figure it out?