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
Vlada [557]
3 years ago
15

Given: △KLM, LM=20 3

Mathematics
2 answers:
egoroff_w [7]3 years ago
6 0

Split the triangle into a 30-60-90 triangle. Since you have LM from that triangle, you can figure out the other sides. Then, using the leg from that triangle, the one next to it is a 45-45-90 triangle, meaning it's isosceles.

KM = 30 + 10√3

KL = 10√6

(sorry i'm not too sure if my "reasons" for statement/reason is correct)

zlopas [31]3 years ago
5 0

Consider the attached diagram. Segment KO is an altitude of the triangle, so KO ⊥ LM. ∠L has measure 180° -105° -30° = 45°, so ΔKOL is an isosceles right triangle.

If we let segment LO have measure 1, then KO also has measure 1 and KL has measure √(1²+1²) = √2 by the Pythagorean theorem.

ΔKMO is half of an equilateral triangle, so KM has measure 2, and MO has measure √(2²-1²) = √3 by the Pythagorean theorem.

Then the ratio of KM to LM is 2:(1+√3) and the ratio of KL to LM is √2:(1+√3). That is, ...

... KL = LM×(√2)/(1+√3) = (20√3)(√2)/(1 +√3)

... KL = (20√6)/(√3 +1) = (20√6)(√3 -1)/(3 -1) . . . . . with denominator rationalized

... KL = 30√2 -10√6 ≈ 17.9315

and

... KM = LM×2/(1+√3) = KL×√2

... KM = (30√2 -10√6)√2

... KM = 60 -20√3 ≈ 25.3590

== == == == == ==

The Law of Sines tells you ...

... KL/sin(M) = KM/sin(L) = LM/sin(K)

Then ...

... KL = sin(M)·LM/sin(K) = sin(30°)·20√3/sin(105°) ≈ 17.9315

... KM = sin(L)·LM/sin(K) = sin(45°)·20√3/sin(105°) ≈ 25.3590

You might be interested in
Solve the inequality.<br> 2(4x - 3)2-3(3x) + 5x?<br> x 20.5<br> x 22<br> (-0, 0.5)<br> O (-0, 2]
muminat

Step-by-step explanatio

3 0
3 years ago
Use the Four-Step Approach to solve the given problem.
V125BC [204]

Answer:30 mi

3s = 2.5(s+2)

3s = 2.5s + 5

3s - 2.5s = 5

.5s = 5

s = 5/.5

s = 10 mph to the beach

:

:

Confirm this by finding the actual distance each way, should be the same

3*10 = 30 mi

Step-by-step explanation:

6 0
3 years ago
Value of log2 8 + log 3(1/3)
Dvinal [7]
There’s no answer choices but i got log(28•3^1/3)
5 0
3 years ago
Mark's ratio is 3 tablespoons sugar to 2 tablespoons milk. Sharri is using 4 tablespoons of sugar to 3 tablespoons of milk. Eve
mezya [45]
Let's calculate for the tablespoons of sugar to tablespoons of milk ratio for Mark, Sharri and Eve.

Mark: 3/2 = 1.5
Sharri: 4/3 = 1.3
Eve: 9/6 = 1.5

From the solution, Eve has an equivalent ratio to that of Mark's.
4 0
3 years ago
How does the position of the decimal point in a quotient as you divide by increasing powers of 10
Digiron [165]
The value decimal point is changing going to the right as you divide a number by 10. For example => 2000.3 / 10 notice the decimal point => 200.013, the value of decimal numbers increases as the value of whole number decreases.Let’s divide again => 200.013 / 10 => 20.0013 , now we already have 4 digits in our decimals. So, simply as we divide the given number by 10, the decimal point moves to the left making the value of whole number decreases and making the number of digits of decimal increase.
4 0
3 years ago
Other questions:
  • Any help if possible Thank you ❤
    11·1 answer
  • How to estimate 19 divided bye 1,425
    10·1 answer
  • What does -43.7 + 9.06 equal?
    15·2 answers
  • Help me please again
    5·1 answer
  • The Valley High School printed 445 tickets for the school play in Spring. Three-fifth
    12·1 answer
  • 4c - 3, when c = -2 ///
    9·1 answer
  • Write the number below in expanded notation<br><br> thirteen thousand five
    6·1 answer
  • If the circle below is cut from the square of plywood below, how many square inches of plywood would be left over? Use π = 3.14,
    8·1 answer
  • write each of the following fraction as equivalent fractions with a denominator of 10 a. 1/2 b. 1/4 c. 3/30 d. 12/30​
    5·1 answer
  • THE SALES TAX ON A TABLE SAW IS $14.85 WHAT IS THE PURCHASE PRICE OF THE TABLE SAW BEFORE TAX IF SALES TAX IS 5.5%
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!