course mth 164 I did not understand the last question and was unable to draw a diagram. õ]§Ì…Í}¼ƒúü©øÌ׌{Ôvassignment #008
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16:30:29 Query problem 7.1.B-10 c = 10 , `alpha = 40 deg, right triangle
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RESPONSE --> ok confidence assessment:
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16:31:10 what are a, b, and B?
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RESPONSE --> a is opposite angle A b is opposit angle b and B is the third angle in the triangle with angle C being the right angle confidence assessment: 3
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16:33:35 Explain how you obtained your solutions.
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RESPONSE --> Given that angle A is 40 degrees then angle B would be 50 degrees since the sum of the angles of a triangle is 180 degrees. Side a would be 6.43 using sin40=a/10 Side b would be 7.66 using cos40=b/10 confidence assessment: 3
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16:33:49 Query problem 7.1.B-24 cliff height 100 feet, angle of elevation 25 deg. Dist of ship from shore.
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RESPONSE --> ok confidence assessment:
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16:34:54 what is the distance so shore?
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RESPONSE --> Using tan theta = opposite/adjacent tan(25)=100/x So, xtan(25)=100 x = 100/tan(25) x = 214 confidence assessment: 3
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16:35:05 Explain how you obtained your solution
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RESPONSE --> Given in previous explaination confidence assessment:
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16:35:39 describe the triangle you used to find this distance and how you solved it
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RESPONSE --> I used a right triangle and used the property of tangent being opposite/adjacent sides of the right triangle confidence assessment: 3
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16:35:58 Query problem 7.1.B-36 guy wire 80 ft long makes an angle of 25 deg with a ground; ht of tower?
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RESPONSE --> ok confidence assessment:
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16:36:24 What is the height of the tower?
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RESPONSE --> 27.4 feet confidence assessment: 3
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16:37:28 Explain how you obtained your solution.
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RESPONSE --> Setting up a right triangle with the guide wire as the hypotenuse and the angle of elevation 20 degrees as an angle. The trig function sin=opposite/hypotenuse sin 20 = height of tower/80 feet solve for height of tower confidence assessment: 3
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16:38:35 query problem 7.1.A-72 length of ladder around corner hall widths 3 ft and 4 ft `theta relative to wall in 4' hall, ladder in contact with walls
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RESPONSE --> ok confidence assessment:
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16:39:17 If the angle is `theta, as indicated, then how long is the ladder?
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RESPONSE --> If theta is given, then the length of the ladder would be tan (theta) = 3/4 confidence assessment: 2
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16:39:43 query problem 7.1.A-78 area of isosceles triangle A = a^2 sin`theta cos`theta, a length of equal side
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RESPONSE --> ok confidence assessment:
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16:49:41 how can we tell that the area of the triangle is a^2 sin(`theta) cos(`theta)?
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RESPONSE --> Drawing a peripedicular bisector to one side and dividing the triangle into two right triangles we can find the area of one of the right triangle using A = 1/2 b*h The base would be 1/2a and the height will be called h. Using trig ratios and theta a base angle, sin theta = h/a Solving for h=a sin theta Using trig ratio for cosine, cos theta = (a/2)/a or cos theta = 1/2 The area of one of these triangle would be A = (1/2)(a/2)(a sin theta) = (1/2)(a^2/2)sin theta Since there is two of these right triangles making up the isosceles triangle multiply the area by 2 and substitute for 1/2 the cos theta you have A = (2)(cos theta)(a/2)(a sin theta) = a^2 cos theta sin theta confidence assessment: 3
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16:50:00 What is the altitude of the triangle?
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RESPONSE --> altitude is h and is a sin theta confidence assessment: 3
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16:50:28 If the triangle is divided into two symmetric halves, then what is the length of a base of one of the halves? What therefore is the length of the base of the whole triangle?
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RESPONSE --> base is a/2 the length of the base of the whole triangle is a confidence assessment: 3
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16:50:46 What therefore must be the area of the triangle?
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RESPONSE --> A = a^2sin theta cos theta confidence assessment: 2
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16:51:07 Query problems 7.2.12 `alpha = 70 deg; `beta = 60 deg, c = 4
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RESPONSE --> ok confidence assessment:
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16:53:18 specify the unknown sides and angles of your triangle.
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RESPONSE --> a = 4.91 b = 4.52 confidence assessment: 3
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16:54:53 Explain how you obtained your results.
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RESPONSE --> Using the Law of Sines a/sin70=4/sin50 to obtain a b/sin60=4/sin50 to obtain b confidence assessment: 3
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16:55:11 Query problems 7.2.28 b = 4, c = 5, `beta = 40 deg
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RESPONSE --> k confidence assessment:
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16:57:15 specify the unknown sides and angles of your triangle.
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RESPONSE --> angle C = 53.5 degrees angle A = 86.5 degrees Side a = 6.21 confidence assessment: 3
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16:58:53 Explain how you obtained your results.
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RESPONSE --> Using law of sines sin C/5=sin40/4; solve for sin C and then use the inverse sin key on the calculator to obtain the angle add angle C and B together and subtract from 180 to find A. Using that value for angle A: a/sin A = 4/sin 40 then solve for a confidence assessment: 3
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16:59:20 Query problems 7.2.40 line-of-sight angles 15 deg and 35 deg with line directly to shore
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RESPONSE --> ok confidence assessment:
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17:01:28 how far is the ship from each Lighthouse and from the shore?
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RESPONSE --> I dont understand the question confidence assessment:
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17:01:40 Explain a you obtained your results.
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RESPONSE --> I dont understand the question confidence assessment:
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17:02:11 Comm on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> I was fine with the questions except for the last one. I couldn't draw a diagram to fit the information so I couldn't solve the problem. confidence assessment:
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