All categories

3 years ago

The height of an object from a distance

Mathematics

1 answer:

olga55 [171]3 years ago

7 0

Y = height
x = distance from tower

tan(19.9) = y/x

tan(21.8) = y/(x-50) ( x is 50 feet closer so subtract 50 from x)

find the tan of the angles:
tan19.9 = 0.362
tan21.8 = 0.400

replace those values in the equations:
0.362 = y /x
0.400 = y / (x-50)

rewrite to solve for height:
0.362x = y
0.400(x-50) = y distribute the 0.400 and rewrite as 0.400x-20 =y

now solve:

0.362x = 0.400x-20

add 20 to each side:
0.362x +20 = 0.400x

subtract 0.362x from each side:

20 = 0.038x

divide both sides by 0.038
x = 20 / 0.038 = 526.3 feet

now that x is known replace x in the original equation and solve for y:

tan19.9 = y /x

0.362 = y / 526.3
y = 0.362 x 526.3
y = 190.5

the height of the tower is 190.5 feet

You might be interested in

PLEASE HELP WILL GIVE BRAINLY POINTS!!!!

Afina-wow [57]

Conner played a total of 6 +3 + 6 = 15 games. He won or tied 6+ 3 = 9 games.

His percentage is 9/15 = 0.6 x 100 = 60%

April played 5+7+4 = 16 games and won or tied 5 +7 = 12 games.

Her percentage is: 12/16 = 0.75 x 100 = 75%

Tony played 20 games and won or tied 14.

His percentage is: 14/20 = 0.7 x 100 = 70%

April has the highest percentage so she is the one who should play.

8 0

3 years ago

THIS IS A MATH PROBLEM BUT SAYING IT IN MY OWN WORDS!?!

Strike441 [17]

927 is your answer 10.3*90 use a calculator brainliest answer me

5 0

3 years ago

Read 2 more answers

Three cell phones towers can be modeled by the points X(6,0), Y(8,4), and Z(3,9). Determine the location of another cell phone t

Marat540 [252]

Answer:

The location of the new cell phone tower is $(h,k) = (3,4)$ , and the equation of the circle is $x^{2}+y^{2} -6\cdot x - 8\cdot y = 0$ .

Step-by-step explanation:

The location of the cell phone tower coincides with the location of a circunference passing through the three cell phone towers. By Analytical Geometry, the equation of the circle is represented by the following general formula:

$x^{2} + y^{2}+A\cdot x + B\cdot y +C = 0$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$A$ , $B$ , $C$ - Circunference constants.

Given the number of variable, we need the location of three distinct points:

$(x_{1},y_{1}) = (6,0)$

$36 +6\cdot A + C = 0$

$(x_{2},y_{2}) = (8,4)$

$80 + 8\cdot A + 4\cdot B + C = 0$

$(x_{3},y_{3}) = (3,9)$

$90 + 3\cdot A + 9\cdot B + C = 0$

Then, we have the following system of linear equations:

$6\cdot A + C = -36$ (2)

$8\cdot A +4\cdot B + C = -80$ (3)

$3\cdot A + 9\cdot B + C = -90$ (4)

The solution of this system is:

$A = -6$ , $B = -8$ , $C = 0$

By comparing the general form with the standard form of the equation of the circunference is:

$A = -2\cdot h$ (5)

$B = -2\cdot k$ (6)

$C = h^{2}+k^{2}-r^{2}$ (7)

Where:

$h$ , $k$ - Coordinates of the center of the circle.

$r$ - Radius of the circle.

If we know that $A = -6$ , $B = -8$ and $C = 0$ , then coordinates of the center of the circle and its radius are, respectively:

$h = -\frac{A}{2}$

$k = -\frac{B}{2}$

$r = \sqrt{h^{2}+k^{2}-C}$

$h = 3$ , $k = 4$ , $r = 5$

The location of the new cell phone tower is $(h,k) = (3,4)$ , and the equation of the circle is $x^{2}+y^{2} -6\cdot x - 8\cdot y = 0$ .

3 0

3 years ago

Pls pls pls pls pls pls pls

mars1129 [50]

The inverse, converse and contrapositive of a statement are used to determine the true values of the statement

<h3>How to determine the inverse, converse and contrapositive</h3>

As a general rule, we have:

If a conditional statement is: If p , then q .

Then:

Inverse -> If not p , then not q .
Converse -> If q , then p .
Contrapositive -> If not q , then not p .

Using the above rule, we have:

<u>Statement 1</u>

Inverse: If a parallelogram does not have a right angle, then it is not a rectangle.
Converse: If a parallelogram is a rectangle, then it has a right angle.
Contrapositive: If a parallelogram is a not rectangle, then it does not have a right angle.

All three statements above are true

<u>Statement 2</u>

Inverse: If two angles of one triangle are not congruent to two angles of another, then the third angles are not congruent.
Converse: If the third angles of two triangle are congruent, then the two angles are congruent to two angles of another
Contrapositive: If the third angles of two triangle are not congruent, then the two angles are not congruent to two angles of another

All three statements above are also true

Read more about conditional statements at:

brainly.com/question/11073037

8 0

2 years ago

Create and describe a function related to your field (or intended field). Give a detailed explanation of the domain (input) and

Andru [333]

An example of a domain that can be illustrated from the information given will be D(x) = 32.

<h3>Domain and range</h3>

An example based on the information given is "A gas tank in John's car can hold 20 gallons of gas and the car gets 32 miles for every gallon".

John fills up the tank and then goes on a trip. In this case, the distance that will be travelled on one tank will be:

D(x) = 32x

In the above function, it should be noted that the number of gallons can be from 0 to 20. Since he gets 32 miles per gallon, the car can travel 640 miles.

In this case, the domain is the number of gallons that can be used. The number of miles will be the range.

Learn more about domains on:

brainly.com/question/2264373

4 0

2 years ago