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
Hal has a steel barrel with a diameter of 6 feet that can be filled to a depth of 4.6 feet with oil. What is the volume of the b
scoray [572]

Answer:

129.996 cubic feet

Step-by-step explanation:

Assuming that the barrel is a perfect cylinder, we can use the formula to find the volume:

\pi(r)^2(h)

First, we have to find the radius, which is:

D = 2r

So the radius is 3 feet, since it is half of the diameter. Then, we plug in the values.

3.14(3)^2(4.6)

Now, we solve. Exponents are first...

3.14(9)(4.6)

Now multiply left to right.

28.26(4.6)

129.996 cubic feet

Therefore, the barrel can hold 129.996 cubic feet of oil. Hope this helps you!

3 0
3 years ago
Can you help me please with this question
GREYUIT [131]

Answer:

132

Step-by-step explanation:

You can tell it is 132 from <ABC because the whole angle is a 180 degree angle now subtract 180-48 which is 132. please give me brainiest

6 0
3 years ago
An empty bulldozer weighed 5 6/8 tons. If it scooped up 6 1/2 tons of dirt, what would be the
muminat

Answer:

12 1/4

Step-by-step explanation:

common denominator between 8 and 2 is 4, adding those up will be 12.25 in decimal form or 12 1/4

8 0
2 years ago
Please help me please help me if you don't know gently move your hand
andrew11 [14]

Answer:

R = 7cm

D = 14cm

CF = C = dπ or C = 2rπ

CV = C = 14π or 2( 7π )

4 0
2 years ago
a recipe for lemonade calls for 1 cup of sugar and 5 cups of water. How much sugar is used per cup of water
lys-0071 [83]
0.20 of a cup of sugar is used per cup of water
8 0
3 years ago
Other questions:
  • Determine whether the equation is always, sometimes, or never true. <br><br><br> 2/3 x + 4 = 2x
    5·1 answer
  • PLEASE SHOW YOUR WORK. thanks
    10·1 answer
  • Please help me with math pleaseeeeee!!!
    13·1 answer
  • Marsha counted 24 birds at the wildlife refuge, and Aamir counted 86 birds. What is the ratio of Aamir’s Burge to Marshall’s bir
    7·2 answers
  • A sphere has a radius of 6. Using 3.14 for pi, what is the volume?
    5·2 answers
  • Solve the exponential equation <br> 1/16=64^4x-3
    12·2 answers
  • Simplify the problems
    5·1 answer
  • If HJ=7x-27, find the value of x
    6·1 answer
  • Find the area of the triangle below.
    14·1 answer
  • Which graph represents the solution set of -2y &gt; 7x + 4?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!