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
tresset_1 [31]
3 years ago
8

Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL

Mathematics
2 answers:
Mice21 [21]3 years ago
3 0

Answer:

KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47

Step-by-step explanation:

Given:

KL ║ NM ,

LM = 45

m∠M = 50°

KN ⊥ NM  

NL ⊥ LM

Find: KN and KL

1. Consider triangle NLM. This is a right triangle, because NL ⊥ LM. In this triangle,

LM = 45

m∠M = 50°

So,

\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}

Also

m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ} (angles LNM and M are complementary).

2. Consider triangle NKL. This is a right triangle, because KN ⊥ NM . In this triangle,

NL=45\tan 50^{\circ}

m\angle KLN=m\angle LNM=40^{\circ} (alternate interior angles)

m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ} (angles KNL and KLN are complementary).

So,

\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08

and

\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47

Natasha_Volkova [10]3 years ago
3 0

Answer:

KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47

Step-by-step explanation:

You might be interested in
a prayng mantis is an interesting insect that can rotate its head 180 degrees.Suppose the praying mantis at the right is 10.5 ce
cricket20 [7]
The fact that it can turn its head 180 degrees is just extra information. They tell us that it is 10.5 cm long. What they're asking for is the length in a mixed number, so 10.5 as a mixed number.
7 0
3 years ago
Read 2 more answers
Liang bought a basket of apples to make pies for her friends. The basket of apples weighed ppp pounds. Before she had time to ma
Bess [88]

Answer:

The equation to describe the situation is  p-3=17.

And, the total weight of the basket of apples was <u>20 pounds</u>.

Step-by-step explanation:

<u><em>The question is incomplete so, the complete question is below:</em></u>

Liang bought a basket of apples to make pies for her friends. The basket of apples weighed p pounds. Before she had time to make the pies, she ate 3 pounds of apples. There are 17 pounds of apples left to make pies. Write an equation to describe this situation. What was the total weight of the basket of apples?

Now, to write an equation to describe the situation. And to find the total weight of the basket of apples.

So, the basket of apples total weighed = p\ pounds.

Liang ate apples weighed = 3 pounds.

And the apples left for the pies weighed = 17 pounds.

Now, to write an equation describing the situation:

p-3=17.

<u><em>Thus, the equation is </em></u>p-3=17.<u><em /></u>

Now, to get the total weight of the basket of apples:

p-3=17\\\\Adding\ both\ sides\ by\ 3\ we\ get:\\\\p=20

<u><em>Hence, the basket of apples total weighed = 20 pounds.</em></u>

Therefore, the equation to describe the situation is p-3=17.

And, the total weight of the basket of apples was 20 pounds.

4 0
3 years ago
I nedd help can anyone ansewer fast please
pashok25 [27]
18. just subtract 49.6 from 54. 54 - 49.6=4.4 He most lose 4.4 pounds. 
19. all you need to do is add 4.6 to 83. 83+4.6=87.6 She will weigh 87.6 pounds
20. divide 910 by 7. 910÷7=130 The dog ate 130 grams per day
21. multiple 4.95 by 5. 4.95×5=24.75 Her total bill was 24.75
22. subtract 12.96 from 20. 20-12.96=7.04 Her change was 7.04
3 0
3 years ago
Your shop employs seven people. Today two people are sick. What fraction represents the employees who are sick
Feliz [49]

Answer:

2/7 of represents employees who are sick

Step-by-step explanation:

Question:

What fraction represents the employees who are sick

Total People = 7

sick people =2

numerator/denominator

2/7

8 0
2 years ago
Abdallah earns AED 30 for each car he washes. He also gives his little brother AED 20 form his weekly earnings. This week, he wa
OlgaM077 [116]

Answer:

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • A school teacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the s
    5·1 answer
  • What is the absolute value from the numbers 3 to -105
    8·2 answers
  • Emma calculated the slope of the downhill hike to be -1/40 her work is shown below determine whether her calculation was correct
    8·1 answer
  • 19 x 50 =_fifties. Please help me
    12·2 answers
  • Arrange the numbers from largest to smallest 2.6 to 2.061 2.61 20.66 6.21​
    5·2 answers
  • What is the value of X?
    5·1 answer
  • Kinsley took out a loan for $2000 with interest rate of 4.8% to pay off the loan in two years she has to make payments of $100 e
    12·1 answer
  • Round 58800 to the nearest cent
    14·1 answer
  • What is this? Please answer if u know what u are doing
    10·1 answer
  • 12 belongs to which set(s) of numbers?o Natural Numbers, Whole Numbers, and Integers onlyNatural Numbers and Whole Numbers onlyo
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!