Download IB Math SL – year 1 - hrsbstaff.ednet.ns.ca

Math 11 Advanced 2012
Working with the tools of Chapter 6
C
b
Law of Cosines:
Used when you know
-three sides (to find an angle)
-two sides and an included angle (to find 3 rd side)
a
a 2  b 2  c 2  2bc cos A
A
c
Law of Sines may
yield an ambiguous
solution
B
Law of Sines:
Used when you know
-two angles and any side (to find another side)
-two sides and a non-included angle (to find another angle)
a
b
c


sin A sin B sin C
1. Farmer Clem is planting sod on his field. The shape of the field is shown below:
If sod costs $12.25 per square meter, what is the cost to sod Farmer Clem's field?
3. In triangle DEF, D = 290, f = 14.2 cm, and d = 7.8 cm. Find angle F.
4. In triangle XYZ, x = 93 cm, y = 41 cm, and z = 81 cm. Find the size of the angle of middle size (not
the largest or smallest angle, but the one in the middle).
5. After the hurricane, the small tree in my neighbor’s yard was leaning. The tree, we noticed, was
leaning at an angle of 4o from the vertical. To keep it from falling, we nailed a metal strap into the
ground 4 feet from the base of the tree. The strap was mounted 3.5 feet up the side of the tree. How
long was the metal strap?
6. A small lake was discovered in rural Nova Scotia. To find the length of the lake, land surveyors
made the following measurements, how long is the lake?
7. Woods is hiking thru the woods (no pun intended) and he comes to the shore of a lake (point L). He
spots a cabin across the water from his current position. To get to the cabin, he traveled 3 km NW, and
then 1.8 km NE.
from point L, describe the direction to (north, east of north, etc) to the cabin. How far from point L is
the cabin?
8. A lighthouse built at sea level is 40.0 m high. From a buoy the angle of elevation to the top of the
lighthouse is
. How far is the buoy from the foot of the lighthouse?
9. Two ships leave port at 4 p.m. One is headed at a bearing of 38 degrees east of north and is traveling
at 11.5 miles per hour. The other is traveling 13 miles per hour at a bearing of 47 degrees east of south.
How far apart are they when dinner is served at 6 p.m.?
10. A forest technician wishes to measure the height of a tree using a hypsometer. At eye level, he finds
the horizontal distance to the tree is 8.0 m, the angle of elevation to the top of the tree is 49.3 degrees,
and the angle of depression to the bass of the tree is 12.7 degrees. According to his approximations,
how high is the tree?
11. Tiger Woods wants to sink a 5.8 metre putt. He gets a little rattled, though, and hits his ball 30 off
line, and the ball only travels 5.5 metres. How far is his ball from the hole?
12. An airplane is increasing its altitude at an angle of
with the horizontal. The speed of the airplane
is 480 km/h. How high will the airplane be in 5 minutes?
13. Use the same strategies we used with acute triangles to prove both
the law of sines and the law of cosines for the obtuse triangle case:
C
You will need these two important formulae:
sin(180 – x) = sin(x)
cos(180 – x) = -cos(x)
h
b
a
A
c
B
c+x
x
Answers:
1. 3350.18
3. 61.96 or 118.04
7. 3.50 (ignore direction for now)
12. 3.50
4. 60.38
8. 57.13
5. 5.50
9. 36.18
6. 154.14
10. 11.10
11. 0.42