Day 15 July 26th: Trigonometry Problem Solving
Opening Exercise: List your top 5 uses for trigonometry in the real world (give a reason why you chose what
you did for number 1)
1. __________________
2. __________________
3. __________________
4. ___________________
5. ____________________
Options: Trigonometry can be used to measure the height of a building or mountains, video games,
construction, flight engineering, physics, archaeologists, criminology, marine biology, marine
engineering, navigation, satellite systems, creation of maps, describing sound and light waves
Example 1: The tallest building in the world is the Burj Khalifa in Dubai (as of April 2019).
If you’re standing on the bridge 250 meters from the bottom of the building, you have to look up at a 73 degree
angle to see the top. How tall is the building? Explain or show your reasoning.
Step 1: what side is the question asking for?
Step 2: label each side hypotenuse, adjacent, and opposite
Step 3: identify the correct trig ratio
Step 4: solve for “x”
Example 2: Find the length of the hypotenuse (AB)
Example 3: 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.
What is the height of the tree?
Exercise 2: 5 min (use your phone to write in the values for sine and cosine)
sin 𝐴 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
sin(15) =
sin(30) =
sin(45) =
sin(60) =
sin(75) =
cos 𝐴 =
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
cos(15) =
cos(30) =
cos(45) =
cos(60) =
cos(75) =
Which pairs match up?
Solve for x, y and z. Test both Column A and Column B.
Do you agree with this conjecture “The sine of ANY acute angle is equal to the cosine of the complementary
angle” Why or why not?