Math 8
CHAPTER 4 TEST
Name:_______________________________________________
ROUND ANGLES TO THE NEAREST TENTH AND SIDES TO THE NEAREST HUNDREDTH, IF NECESSARY.
Solve the problem.
1) Two points A and B are on opposite sides of a building. A surveyor selects a third point C to place a transit.
Point C is 48 feet from point A and 60 feet from point B. The angle ACB is 51°. How far apart are points A and
B?
c2 = 482 + 602 -2 48 60 cos 51
c = 482 + 602 -2 48 60 cos 51
c 47.74ft
2) A guy wire to the top of a tower makes an angle of 57° with the level ground. At a point 34 feet farther from the
base of the tower and in line with the base of the wire, the angle of elevation to the top of the tower is 28°. What
is the length of the guy wire?
180 - 57 = 123
180 - 28 - 123 = 29
x
34
=
sin 28
sin 29
xsin 29 = 30sin 28
34sin 28
x=
sin 29
x
32.92ft
3) Two hikers on opposite sides of a canyon each stand precisely 525 meters above the canyon floor. They each
sight a landmark on the canyon floor on a line directly between them. The angles of depression from each hiker
to the landmark meter are 37° and 21°. How far apart are the hikers? Round your answer to the nearest whole
meter.
tan 37 =
a=
525
a
tan 21 =
525
tan 37
distance =
b=
525
525
+
tan 37
tan 21
525
b
525
tan 21
2064m
4) A sailboat leaves port on a bearing of S72°W. After sailing for two hours at 12 knots, the boat turns 90° toward
the south. After sailing for three hours at 9 knots on this course, what is the bearing to the ship from po`rt?
Round your answer to the nearest 0.1°. (a knot is a unit of measure for speed; like miles per hour)
d = 12knots(2hr) = 24 nautical miles
27
tan(x) =
24
tan-1
d = 9knots(3hr) = 27 nautical miles
27
=x
24
x 48.37
72 - 48.37 23.6
S23.6°W is the bearing
1
5) A new homeowner has a triangular-shaped back yard. Two of the three sides measure 65 ft and 80 ft and form
an included angle of 125°. The owner wants to approximate the area of the yard, so that he can determine the
amount of fertilizer and grass seed to be purchased. Find the area of the yard rounded to the nearest square
foot.
A=
1
65 80 sin 125
2
2130sqft
6) A painter needs to cover a triangular region 62 meters by 69 meters by 72 meters. A can of paint covers 70
square meters. How many cans will be needed?
s=
1
62 + 69 + 72 = 101.5
2
A=
101.5 101.5-62 101.5-69 101.5-72
101.5 101.5-62 101.5-69 101.5-72
70
1960 sqft
28.01
he will need 29 cans
Solve the triangle.
7) a = 8, b = 5, c = 4
A = cos-1
B=9
42 + 52 - 82
24 5
42 + 82 - 52
24 8
C = cos-1
125.1°
30.8°
8 2 + 52 - 4 2
28 5
24.1°
2
Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no
triangle at all. Solve any triangle(s) that results. (10 points if two triangles)
8) B = 41°, a = 4, b = 3
B = 41°, a = 4, b = 3
h
sin 41 =
h = 4sin 41
4
3
4
=
sin 41
sinA1
C1 = 180 - 41 - 61.0
2.6 < 3 therefore there are 2 triangles
4sin 41 = 3sinA1
sinA1 =
4sin 41
3
A1 = sin-1
4sin 41
3
A2 = 180 - 61.0
78.0
119.0°
C2 = 180 - 41 - 119.0
c1
3
=
sin 41
sin 78
c1 sin 41 = 3sin 78
c1 =
3sin 78
sin 41
4.47
c2
3
=
sin 41
sin 20
c2 sin 41 = 3sin 20
c2 =
3sin 20
sin 41
1.56
61.0°
20.0°
Find the area of the triangle.
9)
75°
4
45°
180 - 75 - 45 = 60
A=
4 2 sin(75)sin(45)
2sin(60)
6.31
You can attempt the bonus, ONLY after completing every question on the test.
BONUS. Solve the problem. ( 10 points)
10) A cow is tethered to one corner of a rectangular barn by a 250 foot rope.. The barn measures 30 feet by 30 feet.
Find the maximum grazing area for the cow.
194145 sqft
3