Unit 8, Lesson 9
Finding Unknown Side Lengths
Grade 8
9.2
Activity
Label all the hypotenuses with .
9.3
Activity
- 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?
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Find the value of in the figure.
Student Lesson Summary
The Pythagorean Theorem can be used to find an unknown side length in a right triangle as long as the length of the other two sides is known.
For example, 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 , make substitutions, and solve for the unknown value. Remember that represents the hypotenuse, the side opposite the right angle. For this triangle, the hypotenuse is 10.
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 .
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