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
Flura [38]
3 years ago
11

The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into segments such that their lengths are in rat

io of 1:4. If the length of the altitude is 8, find the length of: (a) Each segment of the hypotenuse (b) The longer leg of the triangle.

Mathematics
1 answer:
Zanzabum3 years ago
6 0

In geometry, it would be always helpful to draw a diagram to illustrate the given problem.

This will also help to identify solutions, or discover missing information.

A figure is drawn for right triangle ABC, right-angled at B.

The altitude is drawn from the right-angled vertex B to the hypotenuse AC, dividing AC into two segments of length x and 4x.


We will be using the first two of the three metric relations of right triangles.

(1) BC^2=CD*CA (similarly, AB^2=AD*AC)

(2) BD^2=CD*DA

(3) CB*BA = BD*AC


Part (A)

From relation (2), we know that

BD^2=CD*DA

substitute values

8^2=x*(4x) => 4x^2=64, x^2=16, x=4

so CD=4, DA=4*4=16 (and AC=16+4=20)


Part (B)

Using relation (1)

AB^2=AD*AC

again, substitute values

AB^2=16*20=320=8^2*5

=>

AB

=sqrt(8^2*5)

=8sqrt(5)

=17.89 (approximately)

You might be interested in
Please help !!!! find the tangent of angle (-)
Troyanec [42]
15/8. Tangent = opposite / adjacent line
8 0
3 years ago
Put thes fallowing numbers in order from largest to smallest -3, -3.5, 6, -6, 0, 1
Verdich [7]
6, 1, 0, -3, -3.5, -6
5 0
3 years ago
Read 2 more answers
Evan went to the park and saw four animals.
dsp73

Answer:

He saw <u>1 duck</u> and <u>3 dogs</u>.

Step-by-step explanation:

Given:

Evan went to the park and saw four animals.

Each animal was either a duck or a dog.

He saw a total of 14 legs.

Now, to find the number of each animal he had seen.

Let the number of duck be x.

And the number of dog be y.

So, total number of animals:

x+y=4\\y=4-x

Now, the total number of legs he did see:

<em>As we know the legs of a duck are 2 and a dog are 4.</em>

2x+4y=14\\2x+4(4-x)=14\\2x+16-4x=14\\-2x+16=14

Adding both sides by -16 we get:

-2x=-2

Dividing both sides by -2 we get:

x=1

The number of duck = 1.

Now, putting the value of x in above equation we get:

y=4-x

y=4-1\\y=3.

The number of dogs = 3.

Therefore, he saw 1 duck and 3 dogs.

4 0
3 years ago
Help me pleaseeee !!
ra1l [238]

Answer:

For x it would be 50 m2

Step-by-step explanation:

8 0
3 years ago
WILL GIVE BRAINLIEST ANSWER!
DENIUS [597]
6. No, the conclusions wrong because 20 out of 50 peoples favourite is drawing which means 20/50 which equals 0.4 times 100 which is 40% not 60%

7. Yes, the conclusion is right because 5/50 is equal to 0.1 times 100 which is 10%
4 0
3 years ago
Read 2 more answers
Other questions:
  • Y^2+8y-9= (y+9) (?)
    14·1 answer
  • Time (in minutes)
    11·1 answer
  • Refer to the park map and check all that apply.
    5·2 answers
  • What is 1/6 divided by 3
    10·1 answer
  • The sum of to numbers is 17, and their difference is 7. What are the two numbers?
    6·1 answer
  • She pac<br>boxes will she need?<br>arpeners
    8·2 answers
  • Solve x2 − 3x = −8. (2 points)
    7·1 answer
  • What is this answer i didn’t go to school for it
    9·1 answer
  • Help me<br> Help me<br> Help me
    11·1 answer
  • Please help i dont get it
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!