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Unformatted text preview: 7% grade. However, if we want
to apply any Trigonometry to a story problem involving roads going uphill or downhill, we
need to view the grade as an angle with respect to the horizontal. In the exercises below, we
ﬁrst have you change road grades into angles and then use the Law of Sines in an application. (a) Using a right triangle with a horizontal leg of length 100 and vertical leg with length 7,
show that a 7% grade means that the road (hypotenuse) makes about a 4◦ angle with
the horizontal. (It will not be exactly 4◦ , but it’s pretty close.)
(b) What grade is given by a 9.65◦ angle made by the road and the horizontal?13
(c) Along a long, straight stretch of mountain road with a 7% grade, you see a tall tree
standing perfectly plumb alongside the road.14 From a point 500 feet downhill from the
tree, the angle of inclination from the road to the top of the tree is 6◦ . Use the Law of
Sines to ﬁnd the height of the tree. (Hint: First show that the tree makes a 94◦ angle
with the road.)
4. Prove that the Law of Sines holds when
12 ABC is a...
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