Math 143 – Final Exam Take Home Portion
Due: Tuesday, Dec. 6, 2016
Name: __________________________
Points earned: _________/ 70
Directions: Place work in the space provided. If you need more room attach work on a separate sheet of
paper. I expect a well-organized and easy to read solution set. Be sure to place enough detail, so as the
reader does not have to make any assumptions to your work. I would like you to work on this
INDIVIDUALLY. You can always ask me questions and I will offer feedback. Happy problem solving and
“May the Force Be With You.”
Problem 1: [6 pts] In the following diagram, find the values of all the missing sides and angles. Please leave
your results correct to one decimal place.
B
22°
18
C
A
7
D
Problem 2: [6 pts]
Find the values of all the missing angles and sides in the triangle below.
Please leave results correct to one decimal place.
C
A
22°
60°
B
Problem 3: [6 pts]
Find the values of all the missing angles in the triangle below. Please leave
results correct to one decimal place.
C
32
A
21
12
B
Problem 4: [9 pts]
In order to find the height of a tree, the logger stands at a point, A, and
measures an angle of elevation of 28°, then they move forward 36 feet to a point, B, and measure
the angle of elevation of 62°. The figure below depicts the situation. Find the height of the tree
accurate to one decimal place.
62°
28°
A
36 feet
B
Problem 5: [9 pts]
A surveyor wishes to find the distance between two points, A and B, that are
on the opposite side of a river. On her side of the river, the surveyor chooses two points, C and D,
that are 80 feet apart and measures the angles shown in the diagram. Find the distance between A
and B correct to one decimal place.
Problem 6: [6 pts]
Find the appropriate missing angle and/or sides to find the area of the
triangle correct to one decimal place.
B
18
34
C
24°
A
Problem 7: [6 pts]
What are the possible value(s) for the angle C in the triangle below which has
an area of 8 square units?
B
4
C
A
16
Problem 8: [6 pts] Answer the following:
(a) Convert the polar coordinate (−4, 210°) into Rectangular (Cartesian) Coordinates.
(b) Convert the Rectangular (Cartesian) Coordinate (−4, −7) into Polar Coordinates.
Problem 9: [8 pts]
Answer the following:
(a) Convert the function 𝑥 2 − 𝑦 2 = 1 into Polar Form.
(b) Convert the Polar equation 𝑟 =
4
1+2 sin(𝜃)
into Rectangular (Cartesian) form.
Problem 10: [8 pts]
Given the vectors: 𝑣⃗ = −2𝑖 − 3𝑗 , 𝑤
⃗⃗⃗ = 3𝑖 + 5𝑗, and 𝑧⃗ = −6𝑖 + 4𝑗,
Evaluate the following:
(a) 𝑣⃗ − 2𝑤
⃗⃗⃗
(b) || 2𝑧⃗ + 3𝑤
⃗⃗⃗ ||
(c) Which combination of vectors are orthogonal?
𝑣⃗ ∙ 𝑤
⃗⃗⃗
𝑤
⃗⃗⃗ ∙ 𝑧⃗
𝑣⃗ ∙ 𝑧⃗
(d) Find the angle between the vectors 𝑤
⃗⃗⃗ and 𝑧⃗