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
frosja888 [35]
2 years ago
15

If p is the incenter of triangle jkl, find each measure

Mathematics
1 answer:
Hunter-Best [27]2 years ago
6 0

Answer:

PO = 7

PM = 7

MJ = 11

∠PJO = 32°

∠KJL = 64°

PL ≈ 18.385

OL = 17

∠PLO = 22°

∠NLO = 44°

∠JKL = 72°

∠MKP = 36°

∠NKP = 36°

∠PKN = 36°

KN = 10

PL ≈ 13.04

PK ≈ 12.21

JL = 28

JK = 21

LK = 27

Step-by-step explanation:

The given parameters are;

The point representing the incenter of the triangle = P

Therefore PO = PM = PN = 7

tan(32°) = PM/JM = 7/JM

∴JM = 7/(tan(32°)) ≈ 11.2

∠PJO = tan⁻¹(7/11)≈ 32.47°

∠PJO = ∠PJM = 32° similar triangles

∠KJL = ∠KJP + ∠PJO = 32 + 32 = 64°

∠KJL ≈ 64°

PL = √(7² + 17²) ≈ 18.385

OL = NL = 17 similar triangles

∠PLO = sin⁻¹(7/18.385) ≈ 22.380°

∠PLO = ∠PLN = 22°

∠NLO = ∠PNL + ∠OLP ≈ 22° + 22° ≈ 44°

∠NLO ≈ 44.380°

∠JKL = 180 - (∠KJL + ∠NLO)

∠JKL = 180° - (64° + 44°) ≈ 72°

∠JKL  ≈ 72°

∠MKP = ∠NKP = 72°/2 = 36°

∠MKP = 36°

∠NKP = 36°

∠PKN = ∠JKL - ∠MKP = 72° - 36° ≈ 36°

∠PKN  ≈ 36°

KN = KM = 10

MJ = OJ = 11

PL = √(7² + 11²) ≈ 13.04

PK = √(7² + 10²) ≈ 12.21

JL = JO + OL = 11 + 17 = 28

JK = JM + MK = 11 + 10 = 21

LK = LN + NK = 17 + 10 = 27

You might be interested in
What is one symbol that is in algebra
daser333 [38]
+,-,=,>,<, and many more, lol i gave more than one :P
7 0
3 years ago
Read 2 more answers
Please someone help
nevsk [136]

Answer:

The answer is 7/3 or 2 1/3

Step-by-step explanation:

1) You change the ÷ into x  (so it will be 7/9 x 1/3)

2) You flip the 1/3 so it will be 3 ( 7/9 x 3)

3) There you have it the answer is 7/3

5 0
3 years ago
Kalvin tosses a paper cup once a day for a year to determine his breakfast cereal. 85% of the time the cup will land on its side
Vlad [161]

Answer:

the cup will land on its side 310 times and it'll land on the end 55 times

Step-by-step explanation:

To determine the amount of times it lands on the side, take the days in a year, 365, and multiply that by .85, which gets you 310. To get the amount of times it lands on its end, just subtract 310 from 365.

3 0
3 years ago
If each inch on the scale drawing equals 5
vazorg [7]

Answer:

5x feet or x times 5.

Step-by-step explanation:

4 0
2 years ago
Use absolute value notation to describe the distance<br> between y and -30 is less than 5.
Tema [17]

Answer:

Step-by-step explanation:

That would be |-30 - y| < 5.

7 0
3 years ago
Other questions:
  • How many liters of a 20% alcohol solution must be mixed with 60 liters of a 90% solution to get a 30% solution?
    11·1 answer
  • Is the square root of 3 irrational or rational ?
    6·1 answer
  • Help Please I don't understand these
    5·1 answer
  • Greta reads 1/2;1 pages per minute when she reads her English homework assignment. At this rate, how long does it take Greta to
    8·1 answer
  • How do you write 592% as a fraction, mixed number, or whole number in simplest form?
    13·1 answer
  • Explain how to find the missing exponent given the base and the value
    11·1 answer
  • Simplify the expression-2(-9g+4)
    13·2 answers
  • PLEASE ANSWER FAST I NEED HELPPP
    7·1 answer
  • If there is a $50 profit on the large cabinets and a $30 profit on the small cabinets.
    9·1 answer
  • Is 5 in the solution set of x + 3 &gt; 8? Explain
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!