course Mth 152 ????????z??€???assignment #023023. `query 23
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05:59:31 **** query 9.4.6 ABC, DEF transversed by EOB at rt angles; OB = EO; show triangles ABO and DOF congruent.
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RESPONSE --> triangle AOB = triangle FOE because vertical angles are equal and SAS cong. property
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05:59:59 SAS: Angle AOB and Angle FOE are equal because they are vertical angles, so we have 2 sides and the included angle of triangle AOB equal, respectively, to 2 sides and the included angle of triangle FOE. Thus, the Side-Angle-Side property holds that triangle AOB is congruent to triangle FOE.
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RESPONSE --> Since they are vertical they are equal
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06:02:17 **** Explain the argument you used to show that the triangles were congruent.
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RESPONSE --> Since the two angles AOB and EOF are vertical the angles are equal and so the SAS property applies
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06:09:04 **** query 9.4.18 ACB and QPR similar triangles, C and P rt angles, A=42 deg **** List the measures of the three angles of each triangle and explain how you obtained each.
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RESPONSE --> A = 42 Q = 42 B = x R = x C = 90 P = 90 42 + x + 90 = 180 x+ 132 = 180 x= 48 42 + 48 + 90 = 180 B & R = 48
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06:10:42 It is given that Angle A = 42 deg. and Angle C = 90 deg. Since all three angles must add up to equal 180 then Angle B = 48 deg. In the second triangle, Angle P must equal 90 deg. since it is a right angle. To find Angle R, 90(48) = 90R sp 4320 = 90R and 48 = R Angle R = 48 deg. To find Angle Q, 90/90 = Q/42 Q = 42 Angle Q = 42 deg.
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RESPONSE --> That is the answers I got but I put that angle A and angle Q were equal
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06:26:28 **** query 9.4.24 similar triangles, corresp sides a, b, 75; 10, 20, 25 **** What are the lengths of sides a and b and how did you obtain each?
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RESPONSE --> a/10 = 75/25 25a = 750 a = 30 b/20 = 75/25 25b = 1500 b = 60
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06:26:58 To find a, 75 (10) = 25a 750 = 25a a= 30 To find b, 75/25 = b/20 1500/25 = 25b/25 so b = 60. a = 30, b = 60 and c = 75. These values are triple the values of the similar triangle.
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RESPONSE --> I saw they were triple but I wanted to work them out for practice.
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06:32:29 **** query 9.4.42 rt triangle a = 7, c = 25, find b **** What is the length of side b and how did you obtain it?
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RESPONSE --> a^2 + b^2 = c^2 7^2 + b^2 = 25^2 49 + b^2 = 625 b^2 = 576 b = 24
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06:33:05 By the Pythagorean Theorem a^2 + b^2 = c^2. So we have 49 + b^2 = 625 Subtract 49 from both sides to get b^2 = 576. Take the square root of both sides to get b = 24.
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RESPONSE --> I used the Pythagorean Theormem formula
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06:36:10 **** What does the Pythagorean Theorem say about the triangle as given and how did you use this Theorem to find the length of b?
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RESPONSE --> If you have a right triangle the legs are equal to the square of the hypotenuse. I put in the numbers given and square them to find the answer
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06:36:28 Student Response: It says the sum of the squares of the lengths of the legs is equal to the square of the hypotenuse. I showed that this is true in the previous problem. I squared the legs and they equaled the hyppotenuse squared.
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RESPONSE --> That is what I did
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06:40:39 **** query 9.4.60 m, (m^2 +- 1) / 2 gives Pythagorean Triple **** What Pythagorean Triple is given by m = 5?
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RESPONSE --> (5^2 +- 1)/2 (25+1)/2 = 26/2 = 13 (25-1)/2 = 24/2 = 12
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06:41:41 ** If m = 5 then (m^2 + 1) / 2 = (5^2 + 1 ) / 2 = 26 / 2 = 13 (m^2 - 1) / 2 = (5^2 - 1 ) / 2 = 24 / 2 = 12 So the Pythagorean triple is 5, 12, 13. We can verify this: 5^2 + 12^2 should equal 13^2. 5^2 + 12^2 = 25 + 144 = 169. 13^2 = 169. The two expressions are equal so this is indeed a Pythagorean triple. **
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RESPONSE --> Those are the answers I got but I didn't check my answer
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06:42:20 **** How did you verify that your result is indeed a Pythagorean Triple?
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RESPONSE --> You plug in you answers to make sure everything is equal.
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06:42:38 Student Answer: The numbers checked out when substituted into the Pythagorean Theorem.
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RESPONSE --> That is what you do
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06:54:05 **** query 9.4.75 10 ft bamboo broken, upper end touches ground 3 ft from stem. **** How high is the break, and how
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RESPONSE --> x^2 + 3^2 = 10^2 x^2 + 9 = 100 x^2 = 91 x = 9.6
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06:54:17 did you obtain your result?
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RESPONSE --> yes x=9.6
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06:57:15 ** If the break is at height x then the hypotenuse, consisting of the broken part, is at height 10 - x. The triangle formed by the vertical side, the break and the ground therefore has legs x and 3 and hypotenuse 10-x. So we have x^2 + 3^2 = (10-x)^2. Squaring the 3 and the right-hand side: x^2 + 9 = 100 - 20 x + x^2. Subtracting x^2 from both sides 9 = 100 - 20 x so that -20 x = -91 and x = 4.55. The break occurs at height 4.55 ft and the broken part has length 10 - 4.55 = 5.45, or 5.45 feet. **
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RESPONSE --> I got 9.6 but I did not equal it to 10-x
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06:57:44 **** How did the Pythagorean Theorem allow you to solve this problem?
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RESPONSE --> I sub the numbers in and worked it from there
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06:58:04 I substituted the numbers into the Pythagorean Theorem.
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RESPONSE --> That is what I did
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07:37:59 **** query 9.4.84 isosceles triangle perimeter 128 alt 48 **** What is the area of the triangle and how did you find
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RESPONSE --> A = 1/2bh A = 1/2(48*43) A = 1/2(2064) A = 1032
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07:38:03 it?
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RESPONSE -->
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07:39:08 ** This problem is algebraically demanding. Your text might have a slicker way to do this, but the following works: If the equal sides are x then the base is 128 - 2 x. The altitude forms a right triangle with half the base and one of the equal sides. The sides of this right triangle are therefore 48, 1/2 (128 - 2x) = 64 - x, and x. The right angle is formed between base and altitude so x is the hypotenuse. We therefore have 48^2 + (64 - x)^2 = x^2 so that 48^2 + (64 - x) ( 64 - x) = x^2 or 48^2 + 64 ( 64-x) - x(64 - x) = x^2 or 48^2 + 64^2 - 64 x - 64 x + x^2 = x^2 or 48^2 + 64^2 - 128 x + x^2 = x^2. Subtracting x^2 from both sides we get 48^2 + 64^2 - 128 x = 0. Adding 128 x to both sides we get 48^2 + 64^2 = 128 x. Multiplying both sides by 1/128 get have (48^2 + 64^2) / 128 = x. Evaluating this expression we end up with x = 50. The base of the triangle is therefore 128 - 2x = 128 - 2 * 50 = 128 - 100 = 28. So its area is 1/2 b h = 1/2 * 28 * 48 = 672. ** DRV
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RESPONSE --> I see now how to work it. I knew it would be as plain as the nose on my face but I couldn't figure it out.
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07:39:14 **** Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE -->
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07:39:16 I had some trouble with the last 2 problems.
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RESPONSE -->
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