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Learning Math Home
Measurement Session 5: Homework
Session 5 Part A Part B Part C Homework
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Session 5 Materials:

Session 5

Problem H1


At a distance of 160 m from a tower, you look up at an angle of 23 degrees and see the top of the tower:

What is the height of the tower?


Problem H2


Compute the height of this extremely steep road at point C for the drawing below:


Problem H3


Draw a side view of the flight path for a glider whose glide angle is 5 degrees. What is the glide ratio?


Problem H4


One glider has a glide ratio of 1:40, while another has a glide angle of 3 degrees. Which glider flies farther? Explain why.


Problem H5


Suppose that a glider has a glide ratio of 1:40. It is flying over a village at an altitude of 230 m, and it's 9 km from an airstrip. Can it reach the airstrip? Explain.


Problem H6


An electricity line pole makes an angle of 75 degrees with the road surface, as shown below:

How much does the road rise over a horizontal distance of 100 m?


Problem H7



Your friend places a mirror 30 ft. from the base of a tall tree. Then she steps back from the mirror until she sees the top of the tree in the mirror's center. What can be said about the angle formed from the treetop to the mirror to the base of the tree, and the angle formed from her head to the mirror to the base of her feet? What do you know about the other angles in the triangles formed below?


How might this information be used to determine the height of the tree?


You know that your friend is 6 ft. tall and that the mirror is 30 ft. from the base of the tree. After your friend moves back 4 ft. from the mirror, she can see the treetop's reflection. How tall is the tree?

Take it Further

Problem H8


Pretend that you are standing at the equator at noon one day, and the Sun's rays are directly overhead (casting no shadow). Meanwhile, your friend, who is located 787 km away, calls you and tells you that at that very moment the Sun is casting a shadow, and that he had measured and calculated that the Sun's rays are coming in at 7.2 degrees. Knowing that there are 360 degrees around the Earth from its center point, use this information to estimate the Earth's circumference. Compare this estimate of the Earth's circumference to today's known value of 40,075.16 km.

Draw some pictures. The 7.2-degree angle will be opposite the length of 787 km. Fifty of these 7.2-degree angles give a complete circle.
   Close Tip


Problems H1-H5 adapted from Looking at an Angle. Mathematics in Context. p. 100. © 1998 by Encyclopedia Britannica Educational Corporation. Used with permission. All rights reserved.

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