Question 173167: Please help me on my homework. I really need your help.
35. From a plane 2,000 m above sea level, the pilot observes two ships in line due west. The angles of depression of the two ships are 60 degrees and 70 degrees. How far apart are the ships?
36. A television antenna is situated atop a hill. From a point 200 m from the base of the cliff, the angle of elevation of the top of the antenna is 80 degrees. The angle of elevation of the bottom of the antenna from the same point is 75 degrees. How tall is the antenna?
37. A 40-cm long pendulum is moved 45 degrees from the vertical. How far did the tip of the pendulum rise?
38. Nuel travels due north from his house for 100 km, then 70 km due west, and then 60 km due north, then he stops. How far is he from from the house?
39. From the 3rd floor of a school building, one can see the top of a house at an angle of elevation of 40 degrees. If the place of observation is 20 m above the ground and 50 m from the house, how high is the house?
40. How long is the midline of an isosceles right triangle when its legs are 20-cm long?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Please help me on my homework. I really need your help.
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Putting so many problems in one posting can make tutors who might help pass your posting. Splitting them up is a better idea, imo.
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35. From a plane 2,000 m above sea level, the pilot observes two ships in line due west. The angles of depression of the two ships are 60 degrees and 70 degrees. How far apart are the ships?
d60 (distance to ship at 60º) = 2000/tan(60) = 1155 meters
d70 = 2000/tan(70) = 728 meters
d60-d70 = 427 meters
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36. A television antenna is situated atop a hill. From a point 200 m from the base of the cliff, the angle of elevation of the top of the antenna is 80 degrees. The angle of elevation of the bottom of the antenna from the same point is 75 degrees. How tall is the antenna?
A = overall height to the top of the antenna
A = 200*tan(80) = 1134 meters
B = height of the base
B = 200*tan(75) = 746 meters
Antenna ht = 1134-746 = 388 meters
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37. A 40-cm long pendulum is moved 45 degrees from the vertical. How far did the tip of the pendulum rise?
If you make a sketch, you see that the pendulum vertical and then moved 45º makes an isosceles triangle with 45º at the top. The other 2 interior angles are 67.5º.
A right triangle from the vertical point under the pendulum to the 45º point has angles of 22.5º and 67.5º.
38. Nuel travels due north from his house for 100 km, then 70 km due west, and then 60 km due north, then he stops. How far is he from from the house?
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39. From the 3rd floor of a school building, one can see the top of a house at an angle of elevation of 40 degrees. If the place of observation is 20 m above the ground and 50 m from the house, how high is the house?
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40. How long is the midline of an isosceles right triangle when its legs are 20-cm long?
The angles have to be 45-45-90. The hypotenuse is sqrt(800) = 20sqrt(2).
If by midline you mean the altitude from the 90º angle, it's half the hypotenuse, = 10sqrt(2).
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I'll do the other problems later.
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