Math 2201 Section 3.3-3.4 Worksheet					Name:__________________

	1.	In DQRS, the values of q, r, and ÐS are known. Write the form of the cosine law you could use to solve for the unknown side.

	2.	Determine the length of w to the nearest tenth of a centimetre.

	3.	Determine the length of d to the nearest tenth of a centimetre.

	4.	Determine the measure of q to the nearest degree.

	5.	Determine the measure of a to the nearest degree.

	6.	In DGHI, g = 30.0 cm, i = 19.3 cm, and ÐH = 53°. 
Determine the measure of h to the nearest tenth of a centimetre.

	7.	In DVWX, v = 52.5 cm, w = 48.0 cm, and x = 61.7 cm. 
Determine the measure of ÐV to the nearest degree.

	8.	A kayak leaves a dock on Lake Athabasca, and heads due north for 2.8 km. At the same time, a second kayak travels in a direction N70°E from the dock for 3.0 km. 
How you can determine the distance between the kayaks?

	9.	In a parallelogram, two adjacent sides measure 17 cm and 14 cm. The shorter diagonal is 11 cm. Determine, to the nearest degree, the measures of the larger angles in the parallelogram.

	10.	Two airplanes leave the Fort Chipewyan airport in Alberta at the same time. 
One airplane travels at 360 km/h. The other airplane travels at 430 km/h. 
About 30 min later, they are 150 km apart. 
Determine the angle between their paths, to the nearest degree.

	11.	A radio tower is supported by two wires on opposite sides. On the ground, 
the ends of the wire are 46.5 m apart. One wire makes a 62° angle with the ground. The other makes a 68° angle with the ground. 
Draw a diagram of the situation. Then, determine the height of the tower to the nearest tenth of a metre.

Worksheet 3.3-3.4
Answer Section

SHORT ANSWER

	1.	ANS:	
s2 = q2 + r2 – 2qr cos S

TOP:	Proving and applying the cosine law		

	2.	ANS:	
w = 27.3 cm

TOP:	Proving and applying the cosine law		

	3.	ANS:	
d = 10.0 cm

TOP:	Proving and applying the cosine law		

	4.	ANS:	
q = 57°

TOP:	Proving and applying the cosine law		

	5.	ANS:	
a = 53°

TOP:	Proving and applying the cosine law		

	6.	ANS:	
h = 24.0 cm

TOP:	Proving and applying the cosine law		

	7.	ANS:	
ÐV = 56°

TOP:	Proving and applying the cosine law		

	8.	ANS:	
Since the measures of two sides and a contained angle are given, I would use the cosine law.

TOP:	Solving problems using acute triangles	

	9.	ANS:	
140°

TOP:	Solving problems using acute triangles	

PROBLEM

	10.	ANS:	
After half an hour, the plane travelling at 360 km/h has gone 180 km and the plane travelling at 430 km/h has gone 215 km.
In a triangle that models the information, the unknown angle q, is opposite the 100 km side.
	1502	= 1802 + 2152 – 2(180)(215) cos q
	22 500	= 32 400 + 46 225 – 77 400 cos q
	–56 125	= –77 400 cos q
		= cos q
	q	= cos–1(0.7251...)
	q	= 43.520...°
The angle between the two airplanes is 44°.

TOP:	Proving and applying the cosine law		

	11.	ANS:	
Let the x and y be the lengths of the wires and h be the height of the tower.
The third angle is 180° – 62° – 68° = 50°.

Use the sine law to determine the length of one of the wires:
	
Use the sine ratio to determine the height of the tower:
	
The tower is 49.7 m tall.

TOP:	Solving problems using acute triangles