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- Today we are going to put a zipline up from the flagpole to the greenhouse, and a zipline up from the school to the greenhouse to see which is fastest! So we've got to measure each object to make sure we know how tall our ladders have to be.
- We looked at the school from a distance of 19 feet. The angle of elevation that we looked up at the school at was 50 degrees. So, we can use sin to figure out how tall the school is. The sin of 50 is equal to 19 divided by h, which is the hypotenuse. H is equal to 19 divided by the sin of 50, which is equal to 24.8 feet, making our school 24.8 feet tall. That's one tall ladder!
- Now we can measure the flagpole. We stood 10.4 feet away from the flagpole, and the angle of elevation that we looked up at was 60 degrees. We can use sin to find out how tall the flagpole is. The sin of 60 is equal to 10.4 divided by the hypotenuse, h. So, h is equal to 10.4 divided by the sin of 60. This means the flagpole is 12 feet tall, which isn't that bad for ladder height.
- Now we have to measure the greenhouse. We stood 8.9 feet away from the greenhouse, and looked up at it at an angle of 15 degrees. We can use cosine to figure out how tall the greenhouse is. The cosine of 15 is equal to 8.9 divided by h, the hypotenuse. H is equal to 8.9 divided by the cosine of 15. So, that means the greenhouse is 9.21 feet tall., and we'll need a ladder that's just about 10 feet tall.
- So, overall we'll need three different ladders. One that is 12 feet tall, one that is 10 feet tall, and one that is 25 feet tall. Let's go set up our zipline!
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