1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
cricket20 [7]
2 years ago
6

Use vectors to find the interior angles of the triangle with the given vertices. (Enter your answers as a comma-separated list.

Enter your answers in terms of degrees. Round your answers to two decimal places.) (−3, −5), (2, 6), (6, 3)
Mathematics
1 answer:
SOVA2 [1]2 years ago
4 0

Answer:

23.92°, 78.503°, and 77.577°

Step-by-step explanation:

The coordinates of the vertices of the triangle are;

X(-3, -5), Y(2, 6), Z(6, 3)

The vectors are;

z = \left \langle 2 - (-3), 6 - (-5) \right \rangle = \left \langle 5, 11  \right \rangle

y = \left \langle 6 - (-3), 3 - (-5)  \right \rangle = \left \langle 9, 8 \right \rangle

x = \left \langle 2 - 6, 6 - 3  \right \rangle = \left \langle -4, 3  \right \rangle

cos (\alpha ) = \dfrac{z \cdot y}{\left |  z \right | \times \left | y  \right |}

Therefore, we get;

cos (\alpha ) = \dfrac{5 \times 9  + 11 \times 8 }{\left |  \sqrt{5^2 + 11^2}  \right | \times \left | \sqrt{9^2 + 8^2}   \right |} = \dfrac{133}{\sqrt{146} \times \sqrt{145} } \approx 0.91409

α = arccos(0.91490) ≈ 23.92°

γ = The angle between -y and x

-y = \left \langle -9, -8 \right \rangle

We get;

cos (\gamma) = \dfrac{-y \cdot x}{\left |  -y \right | \times \left | x  \right |}

Therefore;

cos (\gamma) = \dfrac{-9 \times -4  + -8 \times 3 }{\left |  \sqrt{(-9)^2 + (-8)^2}  \right | \times \left | \sqrt{(-4)^2 + 3^2}   \right |} = \dfrac{12}{\sqrt{145} \times \sqrt{25} } \approx 0.199309

γ = arccos(0.199309) ≈ 78.503°

γ ≈ 78.503°

By angle sum property, β = 180° - (α + β)

β ≈ 180° - (23.92° + 78.503°) = 77.577°

β ≈ 77.577°

The interior angles are;

23.92°, 78.503°, and 77.577°

You might be interested in
Find the quotient.<br><br> 315<br> 33
suter [353]

Answer:

9.54545454545

Step-by-step explanation:

Quotient means the answer when you divided something so I'm assuming you meant divide 315 by 33.

7 0
3 years ago
Read 2 more answers
Choose the expressions that are perfect cubes
Ludmilka [50]

Answer: the second fifth and sixth one

Step-by-step explanation:

4 0
3 years ago
Sven has 11 more than twice as many customers as when he started selling newspapers. He now has 73 customers. How many did he ha
Amiraneli [1.4K]
73-11 = 62

62/2= 31

He started with 31 costumers
3 0
2 years ago
Read 2 more answers
In how many distinct ways can the letters of the word SEEDS be arranged?
8_murik_8 [283]

Answer:

20

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
PLZ HELP WILL GIVE BRAINLIST!!!
FromTheMoon [43]

Answer:

purple=9%

teal=12%

yellow=4%

3 0
3 years ago
Read 2 more answers
Other questions:
  • For each of the following series, tell whether or not you can apply the 3-condition test (i.e. the alternating series test). Ent
    10·1 answer
  • In a water treatment plant, water passes through a cone-shaped filter with a height of 4 m and a diameter of 9 m. The water flow
    11·2 answers
  • How would you write .54545454... (Repeating) as a fraction? Please explain the process!
    15·1 answer
  • Each student wears a name tag while at the aquarium the name tags are rectangles that are three inches long and five inches wide
    15·2 answers
  • How to answer this qestion?
    14·1 answer
  • What is the surface area of the rectangular prism? ( In net form)
    10·1 answer
  • Malik Brooks works 40 hours per week, 52 weeks each year for Metro Delivery. He earns $9.15 per hour. If Malik receives a 4.9% m
    6·2 answers
  • A banker earns a $75,000 annual salary, a 2,35% commission on any approved loans for the bank’s business customers, and a fee of
    11·1 answer
  • Maths Homework - 10A1 - Due 02/12
    10·1 answer
  • How do i solve for this?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!