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
kakasveta [241]
3 years ago
13

Given: △ABC, AB=5sqrt2 m∠A=45°, m∠C=30° Find: BC and AC

Mathematics
1 answer:
Marysya12 [62]3 years ago
6 0

BC is 10 units and AC is 5+5\sqrt{3} units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

  • \frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}
  • AB is opposite to ∠C
  • BC is opposite to ∠A
  • AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ \frac{AB}{sin(C)}=\frac{BC}{sin(A)}

∵ AB = 5\sqrt{2}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}

- By using cross multiplication

∴ (BC) × sin(30) = 5\sqrt{2} × sin(45)

∵ sin(30) = 0.5 and sin(45) = \frac{1}{\sqrt{2}}

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ \frac{AB}{sin(C)}=\frac{AC}{sin(B)}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}

- By using cross multiplication

∴ (AC) × sin(30) = 5\sqrt{2} × sin(105)

∵ sin(105) = \frac{\sqrt{6}+\sqrt{2}}{4}

∴ 0.5 (AC) = \frac{5+5\sqrt{3}}{2}

- Divide both sides by 0.5

∴ AC = 5+5\sqrt{3} units

BC is 10 units and AC is 5+5\sqrt{3} units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

You might be interested in
Which number will have the same result when rounded to the nearest ten or hundred A-97 B-118and5 C-179 D-5091
slamgirl [31]
Lets round it to the nearest ten
A 97 ====> 100
B 118 ===> 120
C 179 ===> 180
D 5091 ==> 5090
No result yet, lets round to the nearest hindred.
A 97 ====> 100
B 118 ===> 100
C 179 ===> 180
D 5091 ==> 5100
As we can see only A give the same result when we round it to the nearest hundred and nearest ten.

5 0
3 years ago
Find the percent of each number 0.9 of 1000
trasher [3.6K]

We can use the is/of = p/100 method here. Our given values are 90% and 1000. Think: "What number is 90% of 1000?" Let's plug in our values.

x/1000 = 90/100

Solve for x.

x = (1000)(0.9)

x = 900

So, 900 is 90% of 1000.

8 0
3 years ago
A​ 12-sided die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} . Find the probability
Free_Kalibri [48]

Answer:

11/12

Step-by-step explanation:

Greater than 1: 2,3.... 12

P(greater than 1) = 11/12

7 0
3 years ago
Read 2 more answers
10(3 + 10u) what is the answer?
photoshop1234 [79]
The correct answer is 30+100u. Hope this helps!!
3 0
3 years ago
Read 2 more answers
the artist goes to the store to buy brushes and small cans of paint. he pays $94. he buys 8 brushes that cost $5 each. the rest
sertanlavr [38]
Pays $94
brushes = $40
94 - 40 = 54
54 ÷ 6 = 9
each can of paint costs $9
7 0
3 years ago
Read 2 more answers
Other questions:
  • Bernite is selling candy for a school fundraiser. The school paid $20 for a box of 15 king size candy bars and bernite sells the
    15·1 answer
  • Pleas help me I have so much more left to do
    11·1 answer
  • Skew lines, rays, and segments will sometimes intersect? true or false
    10·1 answer
  • 1/4 + 1/2 ÷ 3/8 = ?<br><br><br> Please Answer quickly im in a test!
    14·2 answers
  • What is an equation of the line that passes through the point (-2 1) and is parallel to the line whose equation is 4x-2y=8 ?
    7·1 answer
  • What is the square root
    7·1 answer
  • In triangle EFG, angle E equals 8x-16, angle F equals x+8, and angle G equals 2x-10. What is the value of x?
    10·1 answer
  • A park has the dimensions indicated in the diagram. Which expression represent the perimeter of the park?
    10·1 answer
  • Mike uses 22 ounces of lemon juice to make one pitcher of lemonade. He has 572 ounces of lemon juice. How many pitchers of lemon
    11·2 answers
  • Please help!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!