1. Pythagorean Theorem
Skill 61

2. Objective
HSG-SRT.8: Use the Pythagorean Theorem to solve right triangles in applied problems.

3. Let 𝑎=15 and 𝑏=8, find c. 𝑎 2 + 𝑏 2 = 𝑐 2 15 2 + 8 2 = 𝑐 2 c
Example: Solve using the Pythagorean Theorem
Let 𝑎=15 and 𝑏=8, find c.
𝑎 2 + 𝑏 2 = 𝑐 2
= 𝑐 2 c
225+64= 𝑐 2 b
289= 𝑐 2 a
𝒄=𝟏𝟕

4. Let 𝑎=6 and 𝑐=12, find b. 𝑎 2 + 𝑏 2 = 𝑐 2 6 2 + 𝑏 2 = 12 2 c
Example: Solve using the Pythagorean Theorem
Let 𝑎=6 and 𝑐=12, find b.
𝑎 2 + 𝑏 2 = 𝑐 2
𝑏 2 = c
36+ 𝑏 2 =144 b
𝑏 2 =108 a
𝒃=𝟏𝟎.𝟑𝟗

5. Example: Solve using the Pythagorean Theorem
Suppose you are walking to a friend’s house that is 0.7 miles away. You walk 0.35 miles North then turn West. How far must you walk west to reach your friend’s house? b
𝑎 2 + 𝑏 2 = 𝑐 2
𝑏 2 =
𝑏 2 =.49
0.35
0.7
𝑏 2 =0.3675
𝒃=𝟎.𝟔𝟎𝟔𝟐 miles

6. 𝑎 2 + 𝑏 2 = 𝑐 2 6 2 + 8 2 = 𝑐 2 36+64= 𝑐 2 𝑐 2 =100 𝒄=𝟏𝟎 miles
Example: Solve using the Pythagorean Theorem
Suppose you are biking to the fishing dock on the lake. The dock is 6 miles south and 8 miles East. You plan on taking the shortest path. How far must you go to take the shortest path
𝑎 2 + 𝑏 2 = 𝑐 2
= 𝑐 2 c 6
36+64= 𝑐 2 8
𝑐 2 =100
𝒄=𝟏𝟎 miles

7. 61: Pythagorean Theorem Questions Summarize your notes Homework
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