Pythagorean Theorem Skill 61

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

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 15 2 + 8 2 = 𝑐 2 c 225+64= 𝑐 2 b 289= 𝑐 2 a 𝒄=𝟏𝟕

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 6 2 + 𝑏 2 = 12 2 c 36+ 𝑏 2 =144 b 𝑏 2 =108 a 𝒃=𝟏𝟎.𝟑𝟗

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 .35 2 + 𝑏 2 = .7 2 .1225+ 𝑏 2 =.49 0.35 0.7 𝑏 2 =0.3675 𝒃=𝟎.𝟔𝟎𝟔𝟐 miles

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 6 2 + 8 2 = 𝑐 2 c 6 36+64= 𝑐 2 8 𝑐 2 =100 𝒄=𝟏𝟎 miles

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