Thursday, March 17, 2011

How High is the Ceiling?

I wanted a right-triangle solving activity for my basic trig unit in Algebra 2. Students are learning how to find sohcahtoa using different types of information, and how to solve right triangles. We also do a bunch of practice questions, similar to what they'll see on the ACT.

Don't know where, but I remembered seeing this angle-measuring device where you could point at the top of a tall object and pull the trigger and it would tell you the angle of elevation. Then you can solve the right triangle and figure out the height of the object.

I made my own using items from around my classroom. I was super proud of myself.

Supplies needed:  Note card, drinking straw, tape, string, paper clip, and paper protractor.

For the lesson, I projected the picture below. I gave the students some time to look at the picture and to discuss what measurements they would need to solve for the height of the ceiling.

I put them in groups of four and gave them this handout**, a tape measure, and a high-tech angle-measuring device* of their own. They were supposed to start with the height of the ceiling in our classroom and check with me. After approving their process, I sent them out to measure ceiling heights in different rooms around the school.

When they returned to the room, I had posted the actual heights of these ceilings. I was inspired by dy/dan to contact the architects for this information, and I was pleasantly surprised by how quickly they responded and how enthusiastic they were to help out.

Everything went pretty smoothly, but answers were not as close to the actual as I had hoped. A few groups were very close, others as much as 4 feet too short. That gave an opportunity to talk about what changes could be made to achieve better results. Overall I was happy with this activity.

*Prior to posting this, I did a little research and found out this thing is called a clinometer. Then I did a google image search and found a bunch of pictures just like the thing I created. Embarrassing. My husband (Mr. iEverything) found that there is also an "app" for that.

**Definition of "Cafegymatorium", from the handout:  When your school is destroyed by a tornado, this is the room you use as a cafeteria, gym, and auditorium in one. The name has stuck, even though we have a new school now with separate areas for each. :)


  1. Love it! That would be a great activity for beginning trig.

    And cafegymatorium is an interesting name... so which room does it refer to now?

  2. Thanks! The cafegymatorium is part of the old building that was not destroyed, so we used it for everything for awhile. Now it is connected to the new building, and it is just a gym. :)

  3. Ok so I don't understand how this works at all. They are measuring the distance to the wall as the bottom leg of the triangle. And so what is the height of the sighter's eyes supposed to be, the hypotenuse? And how does a clinometer work? I want do this activity but I don't understand.

  4. Hi MissCalcul8! The student looks through the straw at the point where the wall meets the ceiling, then the string on the clinometer measures the angle of elevation to the top of the wall. Then they use that angle and the distance to the wall to solve for the vertical leg of the triangle using tan of angle = opposite side (x)/adjacent side (distance to wall). After they have the opposite side of the triangle, then they add the height of the person's eye to get the full height of the ceiling. I hope that helps! :)

  5. Awesome - I took the kids out a while ago to measure buildings and lampposts, and they really "got" the concept on the last test! I think it's also nice to do an angle of depression activity where you have kids look DOWN from, say, second-floor window or balcony. This way they can practice the contextual procedure for finding difference in height. (My kids dropped a filled water bottle on string earlier in the year to measure our balcony height, so I know my balcony height down to a few cm, and we can use those in our trig calculations.)