MASD1021 – Mathematics
Test 3 – Angles, Triangles and Trigonometry
Student Name: _____Ali Manoor Hoessini_________________________________
Student Number: ____4609400________________________________
Total: /32
Instructions:
Please print clearly – I cannot mark what I cannot read.
Show all your work, including all formulae, steps, logic and calculations used to
obtain your solutions.
Do not round values in the middle of your calculations.
Show all answers as unrounded values.
Only round final answers when required by the question.
All final answers must include units where possible.
1. Solve for the missing angle x.
56º x 85º
𝑥 = 1800 − (850 + 560 ) = 390
2. Solve for angles a, b, and c.
b
45º
a
c
2700
𝑎 = 450 𝑏 = 𝑐 = 3600 − (450 + 450 ) = 2700 = = 1350
2
3. Are the following angles complimentary? YES / NO (circle one)
8º
60º 21º
4. Determine the missing angles and side lengths in the following triangle. Round
side lengths to 2 decimal places if necessary.
c a
42º
b
a=_420______________ A= 42º
b=_480_______________ B=_1800-(420+900)=480___________
c=__900______________ C= 90º
5. Determine the missing angles and side lengths in the following triangle. Round
side lengths to 2 decimal places if necessary.
b
a= 13 ft A=_____________
b=_15.19________ B=_____________
c= 20 ft C= 90º
𝑏 2 = 𝑐 2 − 𝑎2 ⇒ 𝑏 = √𝑐 2 − 𝑎2 = √202 − 132 = √400 − 169 = √231 = 15.19
15.19 13
𝐶 = 900 𝑏 = 𝑎𝑟𝑐𝑡𝑔 ( ) = 49.440 𝑎 = 𝑎𝑟𝑐𝑡𝑔 ( ) = 40.550
13 15.19
𝑎 + 𝑏 + 𝑐 = 900 + 49.440 + 40.550 ≈ 1800
6. A roof has a roof pitch of 5/12 and a run of 15 ft 6 in. What is the height of the
roof, the length of the roof and the slope? Give your length answers (x & y) as
measurable quantities to the nearest 16th of an inch and roof slope (RS) to 1
decimal place. (there are 3 values to calculate)
X 12
Y 5
RS
15’ 6”
𝑐 2 = √52 + 122 = √25 + 144 = √169 = 13
15′6" 𝑦 ′
15′ 6" ∗ 5 1"
= ⇒ (𝑦 ∗ 12 = 15 6*5 ) /12⇒ y = = 77.5=77
12 5 12 2
2
2 2
1"
𝑅𝑆 = 15′6" + 77 ⇒ 𝑅𝑆 = √1862 + 77.52 = √40602.25 = 201.5"
2
7. Find the stud lengths a and b expressed as a measurable quantity, based on the
following diagram:
12
4
76-1/2” a b
16” 16”
𝑎 16" 4 ∗ 16" 1" 7"
= ⇒𝑎= = 5.33 ⇒ 𝑎 = 76 − + 5.33=81.83 = 81
4 12" 12 2 8
𝑏 16" 4 ∗ 16" 1"
= ⇒𝑏= = 5.33" ⇒ 𝑏 = 76 − + 5.33" + 5.33" = 87.16"
4 12" 12 2
8. Determine the missing angles and side lengths of the following triangle. Round
all answers to 2 decimal places if necessary.
5 ft
according the triangle if the side is equal so a^ = b^
𝑎^ + 𝑏 ^ = 1802 𝑎=𝑏 ⇒ 𝑎 + 𝑎 + 90 = 1800 2𝑎 + 90 = 1800 2𝑎 = 180 − 90
90
𝑎= ⇒ 𝑎 = 450 ⇒ 𝑎 = 𝑏 = 450 𝑎 = 450 𝑏 = 452
2
