MATH 113 PRACTICE TEST 1 PART 2
You may use a calculator on this part of the test. You may NOT use a cell phone or computer.
In addition to these problems, be able to work # 73 on page 487 of the book.
10) From a balloon 750 feet high, the angle of
depression to the ranger headquarters is 76.7°.
How far is the headquarters from a point on
the ground directly below the balloon (to the
nearest foot)?
Find the length of the arc on a circle of radius r
intercepted by a central angle θ. Round answer to two
decimal places.
1) r = 50 inches, θ = 20°
2) r = 15.61 inches, θ = 150°
11) From a boat on the lake, the angle of elevation
to the top of a cliff is 25.45°. If the base of the
cliff is 2872 feet from the boat, how high is the
cliff (to the nearest foot)?
Express the angular speed in radians per second.
3) 420 revolutions per second
Solve the problem.
4) A wheel is rotating at 360 radians/min, and the
wheel has a 15.5-inch radius.. To the nearest
FOOT per minute, what is the velocity of a
point on the rim?
12) From a boat on the river below a dam, the
angle of elevation to the top of the dam is
29.283°. If the dam is 708 feet above the level
of the river, how far is the boat from the base
of the dam (to the nearest foot)?
Convert the angle in degrees to radians. Round to two
decimal places.
5) 194°
13) When Mack sits atop a tree and looks down at
his pal Joey, the angle of depression of Mackʹs
line of sight to Joey is 38.7°. If Joey is known to
be standing 17 feet from the base of the tree,
how tall is the tree (to the nearest foot)?
Convert the angle in radians to degrees. Round to two
decimal places.
12π
radians
6)
3
14) From a distance of 48 feet from the base of a
building, the angle of elevation to the top of
the building is 67°. Estimate the height of the
building to the nearest foot.
7) -2.54 radians
Solve the problem.
8) A building 300 feet tall casts a 60 foot long
shadow. If a person stands at the end of the
shadow and looks up to the top of the
building, what is the angle of elevation of the
personʹs eyes to the top of the building (to the
nearest hundredth of a degree)? (Assume the
personʹs eyes are 4 feet above ground level.)
9) A radio transmission tower is 250 feet tall.
How long should a guy wire be if it is to be
attached 10 feet from the top and is to make an
angle of 22° with the ground? Give your
answer to the nearest tenth of a foot.
Solve.
15) What is the angle of elevation of the sun when
a 45-ft flag pole casts a 29-ft shadow? Round
to the nearest tenth of a degree.
Find the measure of the side of the right triangle whose
length is designated by a lowercase letter. Round your
answer to the nearest whole number.
16)
a
29°
b = 17
Use a calculator to find the value of the acute angle θ to
the nearest degree.
17) cos θ = 0.2286
Use a calculator to find the value of the acute angle θ in
radians, rounded to three decimal places.
18) tan θ = 13.2894
Solve the right triangle shown in the figure. Round
lengths to one decimal place and express angles to the
nearest tenth of a degree.
19) A = 40°, b = 46.6
Solve the problem.
20) The mean air temperature T, in F°, at
Fairbanks, Alaska, on the nth day of the year,
1 ≤ n ≤ 365, is approximated by:
2π
(n - 101)) + 25. Find the
T = 37 sin(
365
temperature at Fairbanks on day 105, to the
nearest tenth.
Answer Key
Testname: MATH 113 PRACTICE TEST 1 PART 2
1) 17.45 inches
2) 40.87 inches
3) 840π radians per second
4) 465 ft/min
5) 3.39 radians
6) 720°
7) -145.53°
8) 78.54°
9) 640.7 feet
10) 177 ft
11) 1367 ft
12) 1263ft
13) 14 ft
14) 113 ft
15) 57.2°
16) a = 9 cm
17) 77°
18) 1.496 radians
19) B = 50°, a = 39.1, c = 60.8
20) 27.5° F