Lesson 8Finding Unknown Side Lengths
Learning Goal
Let’s find missing side lengths of right triangles.
Learning Targets
If I know the lengths of two sides, I can find the length of the third side in a right triangle.
When I have a right triangle, I can identify which side is the hypotenuse and which sides are the legs.
Lesson Terms
- hypotenuse
- legs
- Pythagorean Theorem
Warm Up: Which One Doesn’t Belong: Equations
Problem 1
Which one doesn’t belong?
Activity 1: Which One Is the Hypotenuse?
Problem 1
Label all the hypotenuses with
Activity 2: Find the Missing Side Lengths
Problem 1
Find
. Find
. A right triangle has sides of length 2.4 cm and 6.5 cm. What is the length of the hypotenuse?
A right triangle has a side of length
and a hypotenuse of length . What is the length of the other side? Find the value of
in the figure.
Are you ready for more?
Problem 1
The spiral in the figure is made by starting with a right triangle with both legs measuring one unit each. Then a second right triangle is built with one leg measuring one unit, and the other leg being the hypotenuse of the first triangle. A third right triangle is built on the second triangle’s hypotenuse, again with the other leg measuring one unit, and so on.
Find the length,
Lesson Summary
There are many examples where the lengths of two legs of a right triangle are known and can be used to find the length of the hypotenuse with the Pythagorean Theorem. The Pythagorean Theorem can also be used if the length of the hypotenuse and one leg is known, and we want to find the length of the other leg. Here is a right triangle, where one leg has a length of 5 units, the hypotenuse has a length of 10 units, and the length of the other leg is represented by
Start with
Use estimation strategies to know that the length of the other leg is between 8 and 9 units, since 75 is between 64 and 81. A calculator with a square root function gives