Mathematics High School

Two cables, with lengths of 40 feet and 35 feet, are tied from the top of a pole to stakes in
the ground. If the stakes are 30 feet apart, find the height of the pole.

Answers

Answer 1

Answer:

The height of the pole is 33.89 feet.

Step-by-step explanation:

Since the length of the cables are 35 feet and 40 feet respectively, the 40 feet cable being farthest from the pole. We know that they are 30 feet apart. This forms a scalene triangle in which the angle between the 40 feet cable and the distance apart of the cables ( or ground) is the angle of elevation of the pole from the 40 feet cable.

So, we use the cosine rule to find this angle of elevation. So,

b² = a² + c² - 2accosB where a = 40 feet , b = 35 feet, c = 30 feet and B = angle of elevation of top of pole from 40 feet cable.

cosB = (a² + c² - b²)/2ac

cosB = (40² + 30² - 35²)/(2 × 40 × 30)

cosB = (1600 + 900 - 1225)/2400

cosB = 1275/2400

cosB = 0.53125

B = cos⁻¹(0.53125)

B = 57.9°

Since we now have the angle of elevation of the top of the pole from the 40 feet cable, we now find the height h of the pole from

sinB = h/40 since the 40 feet cable, the ground and the pole form a right-angled triangle.

h = 40sinB

h = 40sin57.9°

h = 40 × 0.8472

h = 33.89 feet

So, the height of the pole is 33.89 feet.

Related Questions


Finn looked at 2 websites every 18 hours. At that rate, how long, in
hours, will it take to look at 4 websites? Plz help

Answers

Answer: 1 day, 12 hours (36 hours)

Given that Finn looked at 2 websites every 18 hours, let's solve the problem.

Multiply by 2, because he looks at 4 websites, and 2 x 2 = 4.

18 x 2 = 36.

The answer should be 36. Hope this helps you!

Solve for b.
ab +c=d

Answers

Answer: B = [tex]\frac{-c}{a}[/tex] + [tex]\frac{d}{a}[/tex]

Step-by-step explanation:

you need to get B alone so that would be subtracting everything around it

ab = -c + d

then you need to get that a away from it by dividing both sides by A

B = [tex]\frac{-c}{a}[/tex] + [tex]\frac{d}{a}[/tex]

What would be the fundraiser money kept if they sold 10 t-shirts?

Answers

How much did the t-shirts cost?

Write the word sentence as an equation. Then solve.

The product of 15 and a number x is −75.

Equation:

Solution: x=

Answers

Answer:

As an equation: 15 × x = -75

Solved: x = -5

Step-by-step explanation:

15*x = -75

[tex]\frac{15*x}{15}[/tex] = [tex]-\frac{75}{15}[/tex], Divide by 15 on both sides to solve for x

x=[tex]-\frac{75}{15}[/tex], The 15 in the numerator cancels out with the denominator

x= -5, because 75/15=5

Equation: (-5)(15) = -75

Solution : (x)(15) or (written as, x times 15 )= -75
For x= -5 ( substitute x into -5)
(-5)(15) or written as, negative 5 times 15= -75


help meee please :))))

Answers

Answer:

90°

Step-by-step explanation:

Samuel buys office supplies for his home business. The office supplies cost $175.79 before taxes. The sales tax rate is 8.25%. What is the amount of sales tax Samuel will pay?

Answers

Answer:

175.79* .0825 = 14.50 + 175.79 =  190.29 $190.25

Step-by-step explanation:

The amount of sales tax Samuel will pay is $14.50

Sales tax rate

Given the following information

cost of office supplies = $175.79 sales tax rate = 8.25%

Get the amount of sales tax:

Amount of sales tax = 8.25% of $175.79

Amount of sales tax = 0.0825 * 175.79

Amount of sales tax = $14.50

Hence the amount of sales tax Samuel will pay is $14.50

Learn more on sales tax here: https://brainly.com/question/9437038

(Help!!)Select all the true statements.

Answers

Answer:

the first choice, the second choice, and the last choice

Step-by-step explanation:

5 and 6 because they are alternate angles

2 and 3 because they are corresponding angles

2 and 4 because they are corresponding angles

Is 1,815 a rational number?

Answers

If a number can be represented by a fraction, it is a rational number. So yes, 1815 is a rational number

Answer:

The square root of 1815 is a rational number if 1815 is a perfect square. It is an irrational number if it is not a perfect square. Since 1815 is not a perfect square, it is an irrational number.

Step-by-step explanation:

I comfirmed this, it’s most likely right! (;

A lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey.
Invent four new versions of this lemonade recipe:

1) One that would make more lemonade but taste the same as the original recipe.
2) One that would make less lemonade but taste the same as the original recipe.
3) One that would have a stronger lemon taste than the original recipe.
4) One that would have a weaker lemon taste than the original recipe.
Pls, I'm struggling right now lol.

Answers

Answer:

1. 10 lemons, 4 cups of water and 4 tablespoons of honey

2. 2 1/2 lemons, 1 cup of water and 1 tablespoon of honey

3. 8 lemons, 2 cups of water and 2 tablespoons of honey

4. 2 lemons, 2 cups of water, 2 tablespoons of honey

Answer:

10 lemons, 4 cups of water, 4 tbspoons honey

2 1/2 lemons, 1 cup water, 1 tbspoon honey

7 lemons, 2 cups of water, 1 tbspoon honey

3 lemons, 2 1/2 cups of water, 2 tbspoons honey

Step-by-step explanation:

Can I have Brainliest??? Please!!!

Choose the best representation 8/11

Answers

Ya where are the options....?

Can someone pls help me on this

Answers

Answer:

41.309 kg, 41.32 kg, 41.236 kg

Step-by-step explanation:

I think these are the correct answers.

Ben bought 1 2/3 pounds of jelly beans and 2 3/8 pounds of jolly ranchers. What are the total pounds of candy that Ben bought?

Answers

Answer:

4 1/24

Step-by-step explanation:

1 2/3 +2 3/8 = 5/3 +2 3/8 = 5/3 + 19/8 = 97/ 24 =4 1/24

i need help with this please ​

Answers

Answer:

Yes because the y value is 0 thus the ordered pair is located on the x - axis

Step-by-step explanation:

Yes it is on the x-axis because the y coordinate is 0 meaning it is on the x-axis line

(15) The ratio of boys to girls at the school is 3:5. If there are 160 students at 1 point the school, how many of them are girls? (Do not include any words in your answer.) Your answer​

Answers

Answer:

100

Step-by-step explanation:

160 * (5/8) = 100

- 71 = x/64

One step

Answers

Answer:

x=-4544

Step-by-step explanation:

- 71 = x/64

Multiply each side by 64

- 71 *64 = x/64 *64

x=-4544

Answer:

x=−4544

Step-by-step explanation:

10. 2x =3 - 4y
Contains the point (-4,3)

Answers

Answer:

I don’t know what you’re trying to find but that equation does not contain the point.

Step-by-step explanation:

Express 30 ^1/3 in simplest radical form.

Answers

Answer:

10

Step-by-step explanation:

On Monday morning Sergio Pappas had $14.78 in cash. During the week he earned $45.00 for cutting lawns and $35.75 for yard work, and he spent $25.23 on food and $22.12 on gas.

# Problem Solution
a. What were Sergio’s total earnings for the week?
b. What total amount did he have to spend during the week?
c. What was his balance at the end of the week?

Answers

Answer:

A- 95.53 $         B- 47.35 $     C- 48.18 $

Step-by-step explanation:

45.00+35.75=80.75 (The money Sergio Pappas earned by working.) 80.75+14.78=95.53 (Sergio Pappas money earned by working + initial money.)25.23+22.12=47.35 (Total money lost by Sergio Pappas.)95.53-47.35=48.18 (Total money left by Sergio Pappas over the weekend.)

I tried to explain and help as best I could. I hope you understand. Good luck!

Answer:

A- 95.53 $         B- 47.35 $     C- 48.18 $

Step-by-step explanation:

What is 2 + 2, minus 4?

Answers

Answer:

0

Step-by-step explanation:

2 + 2 = 4 and then 4 - 4 = 0

Answer:

0

Step-by-step explanation:

2 + 2 - 4 =

4 - 4 =

0

Hope this helps.

can someone help me pleaassee

Answers

Answer:

The slope is 1/4.

Step-by-step explanation:

M = Y2 - Y1

X2 - X1

M = 6 - 2

9 - (-7)

M = 4

16

M = 1

4

PLEASE ANSWER QUICK WILL MARK BRAINLIEST

Answers

Answer:

1) A = 80

2) A = 30

Step-by-step explanation:

1) x+50 + 80 + x + 70 = 180

2x+120 = 180

2x = 60

x=30

A = (30) + 50

A = 80

2) x+40 + x+90 + (180-110) = 180

x+40 + x+90 + 70 = 180

2x + 200 = 180

2x = -20

x = -10

A = (-10) + 40

A = 30

Could someone help me to understand this please? It would mean a lot

Answers

Answer:

A: AD

B: 25x15=375

Step-by-step explanation:

A: AD is parallel because the lines are the same.

B: AB = 25mm

BC = 15mm

25x15 = 375mm

The image below is for reference to Question B.

the graph shows the cost of joining a gym in town a

Answers

Answer:

which graph?

Step-by-step explanation:

I need help plz someone help me plz :(

Answers

I’m sorry if this is wrong but since there are 60 minutes in an hour multiply 5•60 = 300+ 300 since there are 2 hours and if she gets a cracker each time maybe 120

True or False: In order to solve the equation below, you would add 6 to each side then
multiply by 8 on each side.
g/8- 6 = -12

Answers

I believe you would add 6 to both sides then divide by 8 instead of multiplying

If 247 players separated into 13 equal teams, how many players will be on each team?

Answers

247 divided by 13 = 19 so there will be 19 players on each team

I need helppp!!!!!!!!!

Answers

Answer: 0.5 and 9

Explanation:

6x + 1 _> 4
6x _> 3
x _> 1/2

-2x + 8 > -12
-2x > -20
x < 10

Thus, 1/2 <_ x < 10 meaning that x is bigger or equal to 1/2 but less than 10.

And if we look at our choice we see that 0.5 and 9 meets the condition

Solve 210 ÷ 30 = ___ using mental math.

7
70
700
7,000

Answers

The answer would be 7

Answer:

7

-by-step explanation:

none needed just do it in your head like 21 devided by 3=7

PLEASE ANSWER AS SOON AS POSSIBLE
The cost of 4 peaches is $4.96. What is the constant of proportionality that relates the cost in dollars, y, to the number of peaches, x? Write the corresponding linear equation.

Answers

4x (4 peaches) = 4y (4.96$)
x (4/4 peaches=1) = y (4.96$ / 4 = 1.24$)
y f(x) = 1.24$

What is –96 ÷ +3? im a little confused when it comes to math

Answers

It’s -32
You’d do 96 divided by 3 with long division and put - in front of the answer
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