Over 2,500 years ago, a Greek mathematician named Pythagoras popularized the concept that a relationship exists between the hypotenuse and the legs of right triangles and that this relationship is true for all right triangles. The Egyptians knew of
this concept, as it related to 3, 4, 5 right triangles, long
before the time of Pythagoras. It was Pythagoras, however,
who generalized the concept and who is attributed with its
first geometrical demonstration. Thus, it has become known
as the Pythagorean Theorem. Apr 14­10:14 AM
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Pythagorean Theorem:
Example 2:
Apr 14­10:18 AM
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Warm up: During Hurricane Sandy, many trees fell all over Rye. Some people decided to take precautions to determine whether or not certain fallen trees would hit their house. My family had a large tree which was 45 ft from the house. If the tree reached the house it would hit it in the exact place that Bella(my dog) sleeps. My question to you is.....Should I move Bella's bed? How can we determine this?
Woof!
Mar 10­8:51 AM
3
Trigonometry is simply the study of right triangles and how the sides
and angles of these triangles are related.
***Notice that trigonometry only deals with right triangles.
Let's focus on angle A....can we state which side is the hypotenuse, the adjacent side, and the opposite side?
Mar 10­9:05 AM
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The Three Trigonometric Ratios
Mar 10­9:08 AM
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How can we remember our three trigonometric ratios? By using....SOH CAH TOA
Mar 10­9:33 AM
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Ex: A ten­foot ladder is leaned against the side of a house in such a way that it makes an angle of 65 with the ground. How high up the house does the ladder reach?(round your answer to the nearest tenth)
er
dd
la
x
65
Mar 10­1:09 PM
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Apr 14­11:19 AM
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Find the value of x if you are standing 400 ft. away and the building is 850 ft.
Building
850 ft
tall. How is this different from the question we just went over?
x
400 ft
Mar 10­1:16 PM
9
The angle of elevation is always measured from the ground up. Think of it like an
elevator that only goes up. It is always INSIDE the triangle.
In the diagram above, x marks the angle of elevation of the top of the tree as seen
from a point on the ground. You can think of the angle of elevation in relation to
the movement of your eyes. You are looking straight ahead and you must raise
(elevate) your eyes to see the top of the tree.
Mar 10­9:08 AM
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The angle of depression is always OUTSIDE the triangle. It is never inside the triangle.
In the diagram below, x marks the angle of depression of a boat at sea from the top of a lighthouse.
You can think of the angle of depression in relation to the movement of your eyes. You are standing at the top of the lighthouse and you are looking straight ahead. You must lower (depress) your eyes to see the boat in the water.
Mar 10­9:11 AM
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1.
Suppose you have been assigned to measure the height of the local water tower.
Climbing makes you dizzy, so you decide to do the job at ground level. From a point 47.3
meters from the base of the water tower, you find that you must look up at an angle of 53
degrees to see the top of the tower. How tall is the tower?
Mar 10­9:15 AM
12
Your pet bird Pete is trapped on a tree branch 6.5 meters above the ground.
Your ladder is only 6.7 meters long. If you place the ladder‛s tip on the branch,
what angle will the ladder make with the ground?
Mar 10­3:59 PM
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Mar 10­3:59 PM
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Ben is flying a kite directly over his friend, Franklin, who is 125 meters away.
The kite strong makes a 39 degree angle with the ground (which is level). How
high is the kite?
Mar 10­4:01 PM
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Apr 14­7:57 AM
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