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MCR 3UIUnit 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)

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.

What is the slant height of the tower?

How high is the tip of the tower to the ground?

a) find x

y

b) find y

x

5.50

320

90m

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.

How far is each from lifeboat?

Argus travels 9.7 mph, Baffin travels 9.4 mph. Who will get there first?

Lifeboat

a) find a & b

b

a

b) time = dist / speed

420

360

B

A

125 miles

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

find swamp length

337.5

285

swamp

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?

F

find the other 2 side lengths

150

N

E

W

S

B

700

250

20.3

A

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

100 / 4 = 25 km

100 km/h for 15 minutes is

Car:

T

Truck:

80 km/h for 20 minutes is

80 / 3 = 26.67 km

25

26.67

480

find the distance between C and T

A

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

700

250

20.3

A

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