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
MAVERICK [17]
2 years ago
14

A wire is stretched from the ground to the top of an antenna tower. The wire is 15 feet long. The height of the tower is 3 feet

greater than the distance d from the tower's base to the end of the wire. Find the distance d and the height of the tower.
Mathematics
1 answer:
Mariana [72]2 years ago
8 0

The distance d is 9 ft and the height is 12ft.

<h3>How to find the distance and the height?</h3>

Here we can model the situation with a right triangle, where the length of the wire is the hypotenuse.

The height is one cathetus and the distance is the other catheti.

Let's define:

  • h = height
  • d = distance.
  • hypotenuse = 15ft

We know that the height of the tower is 3 ft larger than the distance, then:

h = d + 3ft

Now we can use the Pythagorean theorem, it says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.

Then:

d^2 + (d + 3ft)^2 = (15ft)^2

Now we can solve this equation for d:

d^2 + d^2 + 6ft*d + 9ft^2 = (15ft)^2\\\\2d^2 + 6ft*d - 216 ft^2 = 0\\\\d^2 + 3ft*d - 108ft^2 = 0

Then the solutions are:

d = \frac{-3ft \pm \sqrt{(3ft)^2 - 4*(-108ft^2)} }{2} \\\\d = \frac{-3ft \pm 21ft }{2}

We only take the positive solution:

d = (-3ft + 21ft)/2 = 9ft

And the height is 3 ft more than that, so:

h = 9ft + 3ft = 12ft

The distance d is 9 ft and the height is 12ft.

If you want to learn more about right triangles:

brainly.com/question/2217700

#SPJ1

You might be interested in
For g(x)=x^2-x find g(x) when x=-2
torisob [31]

Answer:

g(x) = 6

Step-by-step explanation:

Begin with substuting the x variable with -2, we do this because the question has listed the value of x already.

Using the value of x, -2 we determine g(x).

g(x) = -2^2 + 2

Above is what the equation would look as, after you input the value of -2.

Using pemdas, (parantheses, exponents, multiplication, division, addition, subtraction) solve the equation.

-2^2 = 4

Think of it as -2 * -2, which is why -2^2 is 4.

Add 4 +2.

4 + 2 = 6.

Therefore, the value of g(x) = 6

6 0
3 years ago
(a) determine the null and alternative hypotheses, (b) explain what it would mean to make a Type I error, and (c) explain what i
iren2701 [21]
Null: the mean amount of peanut butter in a jar is equal to 32 oz.
alternative: the mean amount of peanut butter in a Jar is less than 32oz.

type 1 error is is rejecting the null when it is actually true. this means that we would say that the mean amount of peanut butter is not equal to 32 when it actually is.

type 2 error is failing to reject the null when it is actually false. this means that we would say the mean amount of peanut butter is equal to 32 when in reality it is less.
3 0
3 years ago
A retailer buys a radio from the wholesaler for $75.00. He then marks up the price by 1/3 and sells it at a discount of 20 %. Wh
Vikki [24]
He sells it at $80 which gives him a profit of $5!
8 0
3 years ago
Select the correct answer from each drop-down menu. A teacher is making a history test composed of the same number of multiple-c
GaryK [48]

Answer:

Step-by-step explanation:idbdhides by

7 0
3 years ago
Is -30 - (-52) positive or negative?
Luba_88 [7]

Answer:

positive

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • List the the single -digits factor of 924.
    12·1 answer
  • Maths<br> Share £72 in the ratio 2:7
    6·1 answer
  • *HELP ASAP PLEASE *how can u round a decimal number to the nearest whole number?
    8·2 answers
  • Suppose that one card is to be selected from a deck of 20 cards that contains 10 red cards numbered from 1 to 10 and 10 blue car
    5·1 answer
  • ok my question is what is 2912 divided by 12 and i have to show my work so yeah so like do the whole equation please 13892 divid
    14·1 answer
  • Show how to solve a)
    6·1 answer
  • (1)Kamlesh brought a juice bottle of 5 litres. He drank 214 litres
    15·1 answer
  • HELPPPPPPP PLZZZZZZZZZZZZ
    7·1 answer
  • Please help me with this thing please
    11·1 answer
  • How tall will be the entire arrangement in standard ratio?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!