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
lora16 [44]
3 years ago
9

Given: △FKL, FK=a, m∠F=45°, m∠L=30° Find: FL

Mathematics
2 answers:
drek231 [11]3 years ago
8 0

The best way to do this is to draw a picture of ΔFKL and include line segment KM that is perpendicular to FL.  This creates ΔFKM which is a 45°-45°-90° triangle and ΔLKM which is a 30°-60°-90° triangle.

Find the lengths of FM and ML.  Then, FM + ML = FL

<u>FM</u>

ΔFKM (45°-45°-90°): FK is the hypotenuse so FM = \frac{a}{\sqrt{2}} = \frac{a\sqrt{2} }{2}

<u>ML</u>

ΔLKM (30°-60°-90°): from ΔFKM, we know that KM = \frac{a\sqrt{2} }{2} , so KL = \frac{a}{\sqrt{6}} = \frac{a\sqrt{6} }{6}  

<u>FM + ML = FL</u>

(\frac{3}{3})\frac{a\sqrt{2}  }{2} + \frac{a\sqrt{6}  }{6}

= \frac{3a\sqrt{2} + a\sqrt{6} }{6}

Nitella [24]3 years ago
4 0

Answer:

\sqrt{2}\frac{a(\sqrt{3}+2)}{(\sqrt{3}+1)}

Step-by-step explanation:

Given: △FKL, FK=a, m∠F=45°, m∠L=30°

To Find:

Solution: Consider the file attached.

 a perpendicular is drawn to Line FK from L, LP

 in Δ\text{FLP},

\text{KP}=\text{x}

\text{FP}=\text{a}+\text{x}  

as\text{m}\angle \text{PFL}=45^{\circ}=\text{m}\angle\text{FLP}

\text{FP}=\text{a}+\text{x}=\text{LP}

now, in Δ\text{KLP},

\text{m}\angle\text{PKL}=75^{\circ}

\text{tan}75=\frac{\text{LP}}{\text{PK}}

\text{KP}=\text{x}

\text{LP}=\text{x}+\text{a}

2+\sqrt{3}=\frac{\text{a}+\text{x}}{\text{x}}

2\text{x}+\text{x}\sqrt{3}=\text{a}+\text{x}

\text{x}=\frac{\text{a}}{(\sqrt{3}+1)}

\text{LP}=\frac{\text{a}}{(\sqrt{3}+1)}+\text{a}

\text{LP}=\frac{\text{a}(\sqrt{3}+2)}{(\sqrt{3}+1)}

now, in Δ\text{FLP}

\text{LP}=\text{FP}

using pythagoras theorem

\text{LP}^2+\text{FP}^2=\text{FL}^2

2\text{LP}^2=\text{FL}^2

\text{FL}^2=2\frac{a^2(\sqrt{3}+2)^2}{(\sqrt{3}+1)^2}

\text{FL}=\sqrt{2}\frac{a(\sqrt{3}+2)}{(\sqrt{3}+1)}

So, length of \text{FL} is \sqrt{2}\frac{a(\sqrt{3}+2)}{(\sqrt{3}+1)}

You might be interested in
A box has four cards numbered 1, 2, 3, and 4
lora16 [44]
Sample space: H1, H2, H3, H4, T1, T2, T3, T4
All outcomes if the card is three: H3, T3
I was unclear about the last two parts of the question.
6 0
3 years ago
rob is asked to graph this system of equations : 6 x +2y = 5 y = 3x =2 how many times will they intersect
ella [17]

Answer:

The lines will not intersect.

Step-by-step explanation:

I took the test and this was the correct answer, there isnt a solution.

4 0
3 years ago
Read 2 more answers
Your neighbor has a bag with 5 oranges and 7 apples in it. You will be receiving two pieces of fruit from your neighbor. What is
Snezhnost [94]

Answer:

31.82% probability that you will receive 2 apples.

Step-by-step explanation:

The fruits are removed from the bag, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question:

5 + 7 = 12 total fruits, which means that N = 12

7 apples, which means that k = 7

You receive 2 fruits, which means that n = 2

What is the probability, in percent, that you will receive 2 apples, assuming she removes them from the bag in random order?

This is, as a proportion, P(X = 2). So

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 2) = h(2,12,2,7) = \frac{C_{7,2}*C_{5,0}}{C_{12,2}} = 0.3182

0.3182*100% = 31.82%

31.82% probability that you will receive 2 apples.

4 0
3 years ago
The diameter of a circle is 1.4 centimeters. Find its area. Use 3.14 Round to the nearest
NeTakaya

Answer:

Area = 1.54

Step-by-step explanation:

Area = πr^{2}

π = 3.14

diameter = 1.4

radius (half of diameter) = 0.7

Area = 3.14 x 0.7^{2}

Area = 3.14 x 0.49

Area = 1.5386

round to the nearest hundredth:

1.5386 = 1.54

8 0
2 years ago
Read 2 more answers
Can I get help with these two please?
PSYCHO15rus [73]
Hi, hope this helps :)

3 0
3 years ago
Other questions:
  • Which function represents the number of seconds, s, in d days? (Hint: The number seconds in a day is 24 × 60 × 60 = 86,400.)
    13·1 answer
  • Find the value of this expression if x=3
    5·1 answer
  • What is the perimeter of the triangle below? Round to the nearest hundredth.
    12·1 answer
  • Find the value of two number if their difference is 11 and the sum is 55
    9·1 answer
  • Which logarithmic equation is equivalent to the exponential equation below e^2x=7
    11·1 answer
  • Solve for x.<br> 0 &lt; 3x - 6 s 18<br> 0 2 x&lt;0 or x &gt;8<br> x&lt;2 or x &gt; 8
    7·1 answer
  • For the function f defined b f(x)=x^2+2x+3 find f(-x), -f(x), and -f(-x).
    5·1 answer
  • What happens to the value of the expression \dfrac{10}{d} d 10 ​ start fraction, 10, divided by, d, end fraction as ddd increase
    11·1 answer
  • What type of dilation is formed when the scale factor K is greater than one
    6·1 answer
  • Helpppppppppppppppppppppppp
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!