1
Evaluate the following, rounding your answer to two decimal places:
a
9 \sin 63 \degree
b
8 \tan 28 \degree
c
\dfrac{\sin 71 \degree}{7}
d
\dfrac{\cos 7 \degree}{9}
2
Find the value of the following, rounding your answer to the nearest degree:
a
\sin^{-1}(0.7035)
b
\cos^{-1}(0.4447)
c
\tan^{-1}(0.5085)
d
\sin^{-1}(0.2734)
e
\cos^{-1}(0.6484)
f
\tan^{-1}(8.1519)
g
\sin^{-1}(0.8176)
h
\cos^{-1}(0.7035)
3
For each of the following, find \theta to the nearest degree:
a
\sin \theta = 0.5
b
\tan \theta = 1
c
\cos \theta = 0.5
d
\sin \theta = 0.906
e
\tan \theta = 2.2
f
\sin \theta = \dfrac{43}{47}
g
\cos \theta = \dfrac{31}{53}
h
\tan \theta = \dfrac{41}{31}
4
Determine if each statement is true or false.
a
m \angle A =28 \degree
b
For \angle B, the side with length
15 is the opposite side.
c
For \angle B, the side with length
17 is the adjacent side.
d
For \angle A, the side with length
8 is the adjacent side.
e
The hypotenuse is opposite the right angle.
f
The shortest side is opposite the smallest angle.
5
Consider the following triangle:
Select the trigonometric ratio that could be used to solve for the side h.
A
\cos 42 \degree = \dfrac{11}{h}
B
\cos 42 \degree = \dfrac{h}{11}
C
\sin 42 \degree = \dfrac{11}{h}
D
\sin 42 \degree = \dfrac{h}{11}
6
Consider the following triangle:
Select the trigonometric ratio that could be used to solve for x.
A
\cos 30 \degree = \dfrac{\sqrt{10}}{x}
B
\cos 30 \degree = \dfrac{x}{\sqrt{10}}
C
\sin 30 \degree = \dfrac{\sqrt{10}}{x}
D
\sin 30 \degree = \dfrac{x}{\sqrt{10}}
7
Consider the following triangle:
Select the trigonometric ratio that could be used to solve for angle \theta.
A
\sin \theta = \dfrac{24}{12}
B
\sin \theta = \dfrac{12}{24}
C
\cos \theta = \dfrac{24}{12}
D
\cos \theta = \dfrac{12}{24}
8
Rose needs to find \tan 20 \degree without using a calculator. Using the given triangle:
a
Find the length of the adjacent side using the Pythagorean theorem.
b
Find \tan 20 \degree without using a calculator.
9
If \sin 30\degree=0.5, which statement is true?
A
\sin 60\degree=0.5
B
\cos60\degree=0.5
C
\sin60\degree=0.25
D
\cos30\degree=0.5
10
For each triangle:
i
Identify which ratio can be used to find the missing side
ii
Find the missing side, rounding your answer to two decimal places.
a
b
c
d
11
Find the value of the variable in the following triangles, rounding your answer to two decimal places:
a
b
c
d
12
Find the value of the variable in the following triangles, rounding your answer to two decimal places:
a
b
c
d
e
f
13
Solve for all missing sides and angles.
a
b
14
A tree has a height of h. The tip of the shadow of the tree has an angle of 29\degree and its distance from the top of tree is 23 \text{ m}.
a
Select the trigonometric ratio that could be used to solve for height of the tree.
A
\sin 29 \degree = \dfrac{23}{h}
B
\sin 29 \degree = \dfrac{h}{23}
C
\cos 29 \degree = \dfrac{23}{h}
D
\cos 29 \degree = \dfrac{h}{23}
b
Find h, correct to two decimal places.
15
Find the value of the variable(s) in the following diagrams, rounding your answer to two decimal places:
a
b
c
16
Find the value of each variable, rounding your answer to the nearest degree:
a
b
c
d
e
f
g
h
i
j
17
For each triangle, find the value of:
i
x
ii
\theta
a
b
18
Consider the following figure:
a
Find y, rounding your answer to one decimal place.
b
Find x, rounding your answer to one decimal place.
19
Jessica is stringing lights between two lamp posts in her garden on a slope. If the string is 100 \text{ in} long and forms a 30\degree angle with the top post, what is the distance x, between the posts?
A
50\text{ in}
B
57\text{ in}
C
87\text{ in}
D
115\text{ in}
20
A skier is observing a snow fence marking a ski course as they descend a snowy slope. If the snow fence stretches from the top of the slope directly down to the skier as shown:
Which is closest to the total length of the snow fence?
A
25.8\operatorname{ft}
B
55.9\operatorname{ft}
C
64.3\operatorname{ft}
D
78.5 \operatorname{ft}
21
Consider the following figure.
If l is the length of the ladder in meters, find l, to an appropriate level of precision.
22
The person in the figure sights a pigeon above him.
If the angle the person is looking at is \theta, find \theta in degrees. Round your answer to an appropriate level of precision.
23
A ladder measuring 2.36 \text{ m} in length is leaning against a wall. The base of the ladder is 1.25 \operatorname{m} away from the base of the wall.
a
Draw a diagram of the scenario.
b
If the angle the ladder makes with the ground is y \degree, find y to an appropriate level of precision.
24
The diagram shows the side view of a large rectangular billboard structure. Two diagonal iron bars are used to stabilize the billboard. Which is the closest to the measure of x?
A
23\degree
B
45\degree
C
67\degree
D
135\degree
25
A ladder is leaning against the wall. The ladder is measuring 3.46 \text{ m} in length and the distance between the wall and the foot of the ladder is 2.30 \text{ m}.
If the angle the ladder makes with the ground is y \degree, select the trigonometric ratio that could be used to solve for y.
A
\sin y = \dfrac{2.30}{3.46}
B
\sin y= \dfrac{3.46}{2.30}
C
\cos y = \dfrac{2.30}{3.46}
D
\cos y = \dfrac{3.46}{2.30}
26
Two vertices of the triangle represent the two spots on the ground of a schoolyard where two students are standing, looking up at a flagpole from different positions. The angles of elevation from their spot to the top of the flagpole are measured as a\degree and b \degree.
\sin \left(a\degree\right) = \dfrac{5}{13},\, \cos \left(a\degree\right)=\dfrac{12}{13} and \tan\left(a\degree\right) = \dfrac{5}{12}.
-
\sin \left(b\degree\right) = \dfrac{15}{17},\, \cos \left(b\degree\right)=\dfrac{8}{17} and \tan \left(b\degree\right) = \dfrac{17}{8}.
Write a fraction to represent the ratio of the height of the lighthouse to the distance between the two students.
27
Antima needs to find all missing side and angle measures in \triangle ABC.
a
Knowing that she has to find the missing sides and angles of the triangle, in what order should she find them and how?
b
Is this the only possible way she could solve the triangle? Explain.
28
Find the value of the variable(s) in the given diagram, rounding your answer to two decimal places:
29
Consider the following figure:
a
Find x, rounding your answer to two decimal places.
b
Find y, rounding your answer to two decimal places.
30
Consider the given figure:
Find the value of each variable, rounding your answers to two decimal places:
a
x
b
y
c
z
31
Consider the shape given:
a
Find the value of d, rounding your answer to one decimal place.
b
Find the value of f, rounding your answer to one decimal place.
32
\overline{AB} is perpendicular to the radius of the circle with center O.
\overline{OB} is 24 \text{ in} long and cuts the circle at C.
a
Find the length of the radius of the circle, rounding your answer to one decimal place.
b
Find the length of \overline{BC}, rounding your answer to one decimal place.
c
Find the length of \overline{AB}, rounding your answer to one decimal place.
33
Calculate the size of angle DEC.
34
Consider the following figure:
a
Determine which angle has the greater cosine value. Explain your reasoning.
b
Determine which angle has the greater sine value. Explain your reasoning.
c
Determine which angle has the greater tangent value. Explain your reasoning.
35
A ramp of length 311\text{ cm} is being built. The Construction Code says that "ramps shall have a running slope not steeper than 1 unit vertical in 12 units horizontal."
a
Determine the greatest possible angle that the ramp can make with the ground, rounded to two decimal places.
b
Determine the maximum height the ramp could have, rounded to two decimal places.
c
If the ramp covers a horizontal distance of 300\text{ cm}, determine if it would be allowable under the Construction Code.
d
Make a recommendation for the height and horizontal distance covered by the ramp. Explain your reasoning.
