Unit 4, Lesson 7
Applying Ratios in Right Triangles
Geometry
7.1
Warm-up
Calculate the lengths of sides and .
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Calculate the lengths of sides and .
The tallest building in the world is the Burj Khalifa (BURJZH kha-LEE-fah) in Dubai (as of January 2024).
Someone is standing on the bridge about 250 meters from the bottom of the building. They have to look up at about a 73-degree angle to see the top. How tall is the building? Explain or show your reasoning.
The largest masonry building in the world is City Hall in Philadelphia (as of January 2024). If you’re standing on the street about 1,300 feet from the bottom of the building, you have to look up at about a 23-degree angle to see the top. How tall is the building? Explain or show your reasoning.
Using trigonometry and properties of right triangles, we can calculate and estimate measures in different right triangles. We can use these skills to estimate unknown heights of objects that are too tall to measure directly. For example, we can't reach the top of this tree with a measuring tape.
To calculate the height of the tree, we could stand where the angle between the top and bottom of the tree is 10 degrees. Since we know the distance to the tree (the adjacent leg) and would like to know the height (the opposite leg), we need to use tangent. So . In the calculator we can look up that is 0.176. Then we can calculate that is about 17.6. That means the tree is 17.6 feet tall.