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
vodomira [7]
3 years ago
8

Given: ∆ABC, m∠C = 90° m∠BAC = 2m∠ABC BC = 24, AL −∠ bisector Find: AL

Mathematics
1 answer:
emmasim [6.3K]3 years ago
6 0
The answer is that AL is equal to 16.

Given that in triangle ABC, m∠C=90,
it means m∠A +∠B= m∠BAC + m∠ABC = 90
m∠ABC = 90 - m∠BAC
Also given that;m∠BAC = 2m∠ABC
So,
m∠BAC = 2(90 - m∠BAC) = 180 - 2m∠BAC
m∠BAC +2m∠BAC = 180
3m∠BAC = 180
m∠BAC=180/3 = 60
m∠ABC = 60/3 = 30
thus,ΔBAC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:BC=1:√3, AC=BC/√3BC=24, So,
AC=24/√3=8√3AL bisects angle A =>m∠LAC=30
ΔALC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:AL=√3:2AL=2AC/√3=2x8√3/√3=16
You might be interested in
Find the value of s if 57+s=68
olga2289 [7]

Answer

s = 11

Step-by-step explanation:

Find the value of S:

57 + s = 68

Substract 57 from both sides of the equation

s = 68 - 57

s = 11

6 0
3 years ago
Read 2 more answers
Consider the following data set:<br> 11, 6, -2, -4 -5, 0, 8, 15<br> ,<br> Find the median.
s2008m [1.1K]

\bold{ANSWER:}
Median —> 3

\bold{SOLUTION:}

7 0
1 year ago
Use pi=3 calculate the length of a cicumference of a circle with a radius of 5cm
8_murik_8 [283]
Circumference=2pir
r=5
pi=3
circumference=(2)(3)(5)
circumfernce=6(5)
circufmerence=30

answer is 30cm
5 0
3 years ago
Help please. will give Brainly.​
jek_recluse [69]

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The filling in of the formula for the n-th term is pretty straightforward. The attachment shows how simple it is.

The 7th term is found by evaluating the expression for n=7.

  a₇ = 192

8 0
2 years ago
grace and her friends were to roll the two dice 100 times, how many of the 100 times could they expect to roll the same number o
LenaWriter [7]

Answer:

The probability of both dice having the same number is 636, as there are 36 different outcomes, 6 of which have two of the same number, i.e. (1,1),(2,2),....

The expected number of rolls of this type in 100 pairs of dice rolls is 100∗636

4 0
2 years ago
Other questions:
  • Write an algebraic expression for the product of two and the sum of four and twice a number. Plz help! :(
    15·1 answer
  • Mrs .Nelson has a rectangular flower box that is 5 feet long and 2 feet tall. she wants the width of the box to be more than 5 f
    11·1 answer
  • Each year the local country club sponsors a tennis tournament. Play starts with 128 participants. During each round, half of the
    7·1 answer
  • SORRY PLEASE DONT BAN ME BRAINLY!!!!!!
    8·2 answers
  • Which ordered pair is the vertex of y = |x + 2| - 1
    6·1 answer
  • The price of a new car is $23,000. If the sales tax rate is 3%, then how much sales tax is being charged? What is the total cost
    7·2 answers
  • Helpppppp pleaseeee I have to ansswer Find the area of the shaded region
    10·1 answer
  • Kay is using cone-shaped party hats as popcorn holders. The party hats have a diameter of 10 inches and a height of 9 inches. Ho
    8·2 answers
  • HELP ME PLZ !!!!!!!!
    12·1 answer
  • A gallon of gas costs $2.89. Ms. Sizemore filled up her tank with 12 gallons of gas. How much did she pay?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!