MCR3U - 4.2 - Applications

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Learning Goal: To apply SOHCAHTOA, Sine Law and Cosine Law to real­life situations.
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Apr 15­8:55 PM
When do we need stuff?
SINE LAW:
33
110
13
5
x
115
6
x
COSINE LAW:
110
6
13
8
5
x
x
So, when do we
use the COSINE
LAW???
7
­ when you have no corresponding side angle pairs
­ when you have two sides and the angle in between
­ when you have only 3 sides
Sep 9­9:22 PM
1
A helicopter hovers directly above the landing pad on the roof of a 125 m high building. A
person is standing 145m from the base of the building. the angle of elevation of the
helicopter from this person is 58 degrees. assume the landing pad is at the edge of the
roof closest to the person on the ground. how high is the helicopter hovering about the
landing pad?
32
125
58
145m
Apr 17­9:46 PM
Due to wind, a tree grew so that it leaned 8 degrees from the vertical. From a point on
the ground 28 meters from the base of the tree, the angle of elevation to the top of the
tree is 24.6 degrees. What is the height of the tree?
8 82
24.6
28
Apr 17­9:47 PM
2
X
2.3km
6.2km
5.9km
Apr 17­10:04 PM
THE RELAY
Apr 16­9:30 PM
3
1. From a point on the ground 500 m from the base of a building, it is observed that the angle of elevation to the top of the building is 24° and the angle of elevation to the top of a flagpole atop the building is 27°. Find the height of the building and the length of the flagpole. 2. The angle of elevation to the top of a building, C, from two points A and B on level ground are 50° and 60° respectively. The distance between points A and B is 30 meters. Points A, B and C are in the same vertical plane. Find the height h of the building. 3. A boy is flying two kites at the same time. He has 38 m of line out to one kite and 42 m to the other. He estimates the angle between the two lines to be 30°. Approximate the distance between the kites. 4. Two tugboats that are 12 m apart pull a barge. If the length of one cable is 21 m and length of the other cable is 23 m, find the angle formed by the two cables. 5. Find the area of a triangle with sides of length 5, 6, and 8 units. 6. A ship leaves port at 1 pm traveling north at the speed of 30 miles/hour. At 3 pm, the ship adjusts its course 20 degrees eastward. How far is the ship from the port at 4pm? 7. The posts of a hockey goal are 2.0 m apart. A player attempts to score by shooting the puck along the ice from a point 6.5 m from one post and 8.0 m from the other post. Within what angle must the shot be made? Apr 17­10:09 PM
4