WP8a
Practice - The Pythagorean Theorem
TRY TO ANSWER IN TWO AND A HALF MINUTES.
QUESTIONS
QUESTIONS
1. A tower casts an 11' shadow. The distance from the top of the tower to the tip of the shadow is 61'. How tall is the tower?
2. You want to put a diagonal brace between opposite corners of a rectangular frame. The frame measures 6' by 12'. How long should you cut the diagonal brace? Round to the nearest hundredth of a foot.
3. You lean a 12' ladder against the wall. The bottom of the ladder is 4' from the bottom of the wall. How high on the wall is the top of the ladder?
4. A right triangle has a hypotenuse of 25. One short side is 15. What is the other side?
5. A right triangle has a hypotenuse of 7. One short side is 3. What is the other side?
ANSWERS
1. 61 x 61 = 3721. 11 x 11 = 121. 3721 - 121 = 3600. √ 3600 = 60.
2. 6 x 6 = 36. 12 x 12 = 144. 36 + 144 = 180. √ 180 = 6√ 5 = 13.41.
3. 12 x 12 = 144. 4 x 4 = 16. 144 -16 = 128. √ 128 = 8√ 2 = 11.31.
4. This is a 3-4-5 triangle, with sides of 15, 20 and 25. You can see that the third side is 20 without calculations.
5. 7 x 7 = 49. 3 x 3 = 9. 49 - 9 = 40. The square root of 40 is 6.3, rounded to the nearest tenth.
CALCULATOR STEPS
These steps show the steps for both (a) the square root method (2nd and x²) and (b) the fractional exponent method (exp and n/d).
1a. (root ) Press on and clear. Press 2nd and x². Press ( . Key in 61. Press exp. Key in 2. Press right. Press - . Key in 11. Press exp. Key in 2. Press right. Press ). Press enter. The screen should show "60". Be sure to press right after the exponent.
1b. (exponent) Press on and clear. Press ( . Key in 61. Press exp. Key in 2. Press right. Press - . Key in 11. Press exp. Key in 2. Press right. Press ). Press exp and n/d. Key in 1. Press down. Key in 2. Press right. Press enter. The screen should show "60". Be sure to press right after the exponent.
2a. (root) Press on and clear. Press 2nd and x². Press ( . Key in 6. Press exp. Key in 2. Press right. Press + . Key in 12. Press exp. Key in 2. Press right. Press ). Press enter. The screen should show "6√ 5". Press <> . The screen should show "13.416..." Be sure to press right after the exponent.
2b. (exponent) Press on and clear. Press ( . Key in 6. Press exp. Key in 2. Press right. Press + . Key in 12. Press exp. Key in 2. Press right. Press ). Press exp and n/d. Key in 1. Press down. Key in 2. Press right. Press enter. The screen should show "6√ 5". Press <> . The screen should show "13.416..." Be sure to press right after the exponent.
3a. (root) Press on and clear. Press 2nd and x². Press ( . Key in 12. Press exp. Key in 2. Press right. Press - . Key in 4. Press exp. Key in 2. Press right. Press ). Press enter. The screen should show 8 √2. Press <> . The screen should show "11.31...".
3b. (exponent) Press 2nd and x². Press ( . Key in 12. Press exp. Key in 2. Press right. Press - . Key in 4. Press exp. Key in 2. Press right. Press ). Press exp and n/d. Key in 1. Press down. Key in 2. Press right. Press enter. The screen should show 8 √2. Press <> . The screen should show "11.31...".
4. The calculator is not necessary.
- 5a. (root) Press on and clear. Press 2nd and x². Press ( . Key in 7. Press exp. Key in 2. Press right. Press - . Key in 3. Press exp. Key in 2. Press right. Press ) . Press enter. The screen should read "2 √ 10". Press <> . The screen should read "6.3...".
- 5b. (exponent) Press on and clear. Press ( . Key in 7. Press exp. Key in 2. Press right. Press - . Key in 3. Press exp. Key in 2. Press right. Press ) . Press exp. Press n/d. Key in 1. Press down. Key in 2. Press right. Press enter. The screen should read "2 √ 10". Press <> . The screen should read "6.3...".
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