Transcript Wed Dec 5 - Sin Law and Cos Law Problem Solving

MCR 3UI
Unit 6 – Day 2
Today you will be solving problems using trigonometry.
Some of the questions require you to draw a diagram .
Students are either very good or very bad at this so we will be making the
diagrams as a class.
Today’s HW is Pg. 522 # 7cd, 10 – 12 , 14, 15, 20
(This is different than what is on the outline)
Diagrams are required for questions 10 – 12, 14 and 15.
The title for today is
Problem Solving with Sin Law and Cos Law – Day 2
Leave approximately 3/4 of a page blank for questions 7cd
(if you want your homework to be in order)
pg. 523 # 10
A tower leans toward the south at an angle of 5.50. One day, its shadow is 90m long,
and the angle of elevation from the tip of the shadow to the top of the tower is 320.
a) What is the slant height of the tower?
b) How high is the tip of the tower to the ground?
a) find x
x
320
90m
y
5.50
b) find y
pg. 523 # 11
Two ships, the Argus and the Baffin , are 125 miles apart. The captain of the Argus
calculates that the angle formed between the Baffin, itself and the lifeboat is 360. The
captain of the Baffin calculates that the angle between the Argus, itself and the lifeboat
is 420.
a) How far is each from lifeboat?
b) Argus travels 9.7 mph, Baffin travels 9.4 mph. Who will get there first?
Lifeboat
b
a) find a & b
a
b) time = dist / speed
A
420
360
125 miles
B
pg. 523 # 12
Surveyor starts at one end of the swamp and walks in a straight line, 450 paces and
turns 600 towards the swamp. She then walks in another straight line, 380 paces before
arriving at the other end of the swamp. One pace is about 75 cm. How long is the
swamp in meters?
75 cm = 0.75m
450 x 0.75 = 337.5m
380 x 0.75 = 285m
600
337.5
285
swamp
find swamp length
pg. 523 # 14
Two forest fire towers, A and B are 20.3 km apart. The bearing from A to B is N700E. The
ranger in each tower observes a fire . The bearing from tower A is N250E. The bearing
from tower B is N150W. How far is the fire from each tower?
N
F
find the other 2 side
lengths
E
W
150
S
B
250
A
700
20.3
pg. 523 # 15
Two roads intersect at an angle of 480. A car and a truck have an accident and then
leave on different roads. The car travels 100km/h and the truck travels 80 km/h. Fifteen
minutes after the accident the car is pulled over. Twenty minutes after the accident the
truck is pulled over. How far apart are the vehicles at this time?
C
T
Car: 100 km/h for 15 minutes is 100 / 4 = 25 km
Truck: 80 km/h for 20 minutes is 80 / 3 = 26.67 km
25
26.67
480
A
find the distance between C and T
Today’s HW is Pg. 522 # 7cd, 10 – 12 , 14, 15, 20
(This is different than what is on the outline)
As a bonus: Solve # 17
If you get a wrong answer but think your process is correct, do not erase the whole thing.
It could be a very small mistake.
I am collecting your homework (for actual marks).
pg. 523 # 14
F
You can figure out all the angles if you
make right triangles.
150
B
250
A
700
20.3