A 12-meter ladder leans against a building forming a 30° angle with the building.

Exactly how high is the ladder on the building in meters? Round to the nearest hundredth
(2 digits after the decimal).

Answers

Answer 1

Answer:

will show you two (2) ways to solve this problem.

A diagram is needed to see what is going on....

 

Without loss of generality (WLOG)

The wall is on the right. The ladder leans against the wall

with a POSITIVE slope, from SW to NE (quadrant 3 to quadrant 1).

The measure from the bottom of the ladder to the wall is 6.

 

 

Option 1:

 

The ladder, ground and wall form a right triangle.

 

The hypotenuse (ladder) is 14 feet.

 

 The bottom of the ladder is 6 feet from the wall,

  so the base of this right triangle is 6 feet.

 

The top of the ladder to the ground represents

the missing leg of the right triangle.

 

The pythagorean theorem applies, which says

 6^2 + h^2 = 14^2   where h is the height

                                 of the top of the ladder to the ground

 

36 + h^2 = 196

 

 h^2 = 196 - 36

 

h^2  = 160

 

h = sqrt(160)

 

   = sqrt(16 * 10)

 

    = sqrt(16)* sqrt(10)

 

    = 4*sqrt(10) <--- exact answer

 

    = 4 * 3.16227766016838....

 

     = 12.64911....

 

    12.65 <--- rounded to 2 digits as directed

 

----------------------------------------------

Option #2: using trig

 

With respect to the angle formed by the bottom of the

ladder with the ground

  cos T = 6/14 = 3/7  

 T = inverse-cosine(3/7) = 64.623006647 degrees

 

 sin(64.623006647) = h/14

 

 h = 14*sin(64.62300647) = 12.6491106 <--- same answer                        

hope this helps

Step-by-step explanation:


Related Questions

1. Which table below represents a function that is not proportional? ​

Answers

I belive it is b

Step-by-step explanation:

I hope this help

I need help in this question :(

Answers

Answer:

c

Step-by-step explanation:

If you rotate the triangle U lines up with E and T lines up with D

Which graph represents this system?
y = 3
X+ y = 4
18
6
6
5
2
23
4 5 6
1
g
92
Mark this and return

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Your mommmmmmmmmmmmmmmmmmmmmm

-19 < 5x + 6 < 26
can someone please help

Answers

Answer:

D

Step-by-step explanation:

If f(x) = x^3 + 13x^2 + 46 x + 48 and x + 8 is a factor of f(x) find all of the zeroes of f(x) algebraically

Answers

If x + 8 is a factor, we can factor it out from f(x).

f(x) = (x+8)(x²+5x+6)

     = (x+8)(x+2)(x+3)

The zeroes of f(x) are -8, -2 and -3.

Two similar rectangles have a scale factor of 3:2 the perimeter of the small rectangle is 50 feet.What is the perimeter of the large rectangle measured in feet

Answers

Answer: 75 feet

Step-by-step explanation:

From the question, we are informed that two similar rectangles have a scale factor of 3:2 and that the perimeter of the small rectangle is 50 feet.

The perimeter of the large rectangle measured in feet will be calculated as:

= 3/2 × 50

= 150/2

= 75 feet

Please help

Find the inverse function.
8x – 4y = 24

Answers

Answer:

Simplifying
8x + -4y = 24

Solving
8x + -4y = 24

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4y' to each side of the equation.
8x + -4y + 4y = 24 + 4y

Combine like terms: -4y + 4y = 0
8x + 0 = 24 + 4y
8x = 24 + 4y

Divide each side by '8'.
x = 3 + 0.5y

Simplifying
x = 3 + 0.5y

God bless you and have a beautiful rest of your day!

BRAINLIEST IF RIGHT If m∠BFG=(2x+146)∘, and m∠BCG=(4x+238)∘, what is the value of x? HELP!

Answers

Answer:

-34

Step-by-step explanation:

The value of x from the figure is -46.

What is a parallelogram?

Parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

From the figure,

BCFG is a parallelogram,

So,

m∠BFG = m∠BCG

Now,

2x + 146 = 4x + 238

4x - 2x = 146 - 238

2x = -92

x = -46

Thus,

The value of x is -46.

Learn more about parallelograms here:

https://brainly.com/question/1563728

#SPJ3


What is the slope of the line shown in the graph
A). -1
B). -2
C). -1/2
D). -2

Answers

Answer:

there are two options that say -2.

The answer is -2 so both options b and d.

Is 3 1/2 cups more or less than 1 liter? Explain or show your reasoning

Answers

3 1/2 is less because 1 liter in cups is 4.227

Find the equation of the line with x-intercept ( – 2,0) and y-intercept (0, – 1).

Answers

Answer:

y=-1/2x-1

Step-by-step explanation:


6 Alyssa plans to run mile on a trail. At one point, she sees
that she is at mile marker 0.3. How much farther does she
have to run?

Answers

Answer:

She needs to run a distance of 700 to reach 1000 (1000 is the mile mark)

in this questions form she needs to run 0.7 more to finish her mile

Step-by-step explanation:

A student was asked to name all values of n that make the relation a function. Correct the error.
{(2,8), (6,0), (4,2), (2n,n)}
n can be any value except 2,6, or 4

Answers

Answer:

1,2,3,

Step-by-step explanation:

I GOT THE ANSWER WRONG AND IT TOLD ME THE CORRECT ANSWER

pls help i need to know this so thanks if u do!

Answers

Answer:

124181114201 and 1/21/8 cubic meters

Answer:

Step-by-step explanation:

Basically you have to substitute the values.

-(-125) = ___


can someone answer this

Answers

Answer:

125

Step-by-step explanation:

the minus and negative sign basically cancel each other out and/or combine to make + sign for positive

Mike earns $70 per day. He received a 25% increase in pay. How much money is Mike now making per day?

Answers

I think it’s $175
70 times 25/100=175

Rodrigo leaves a $23. 76 tip on a $132 bill. What percent tip did he leave?

Answers

Step-by-step explanation:

23.76/132 = 0.18

18% tip

PLEASE HELP!!! I WILL GIVE BRAINLIEST!!!(look at pic)

The length of a rectangle is x feet. Its width is (x - 5) feet. Label the rectangle to represent
this situation.

Answers

Answer:

uh the pic is all black? i need the pic to find out whats the awnser is

Please please please please help me someone

Answers

Answer:

That incorrect

Step-by-step explanation:

Yes

What is the equivalent expression that represents its perimeter 80x-64 HELP!


1)80x-64

2) 8x

3) 10x-8

4)8(10x-8)

Answers

Answer:

4. 8(10x-8)

Step-by-step explanation:

An "equivalent expression" has the same value to that of the original expression.

8(10x-8) is an equivalent expression of 80x-64 because both have the same value.

Let's solve.

8(10x-8) = 80x-64

8x10x-(8x8) = 80x-64

80x-64 = 80x-64

This makes the answer correct.

Choice 1 is just the same expression, so it's not an equivalent expression.Choice 2 and 3 are not equivalent expressions as well.

Jessie designed a sculpture that is shaped like a circle. The circumference of the sculpture is 10π meters. Which measurement is closest to the area of the sculpture in square meters? 31.4 m² 78.5 m² 62.8 m² 314 m²

Answers

I believe that it is 31.4, but please correct me if I'm wrong.

The required area of the sculpture that is shaped like a circle is [tex]78.5m^{2}[/tex].

Given that,

Jessie designed a sculpture that is shaped like a circle,

The circumference of the sculpture is 10π meters.

We have to determine,

Which measurement is closest to the area of the sculpture in square meters.

According to the question,

Circumference of the circle = [tex]2\pi r[/tex]

Where, circumference = [tex]10\pi[/tex]

Then,

[tex]10\pi =2\pi r \\\\r = \dfrac{10\pi }{2\pi }\\\\r = 5m[/tex]

Therefore,

Jessie designed a sculpture that is shaped like a circle.

Area of the circle = [tex]\pi r^{2}[/tex]

Where, r = 5m

Then,

Area of the circle is given by,

[tex]= \pi r ^{2}\\\\= 3.14 \times (5)^{2}\\\\= 3.14 \times 25\\\\= 78.5m^{2}[/tex]

Hence, The required area of the sculpture that is shaped like a circle is [tex]78.5m^{2}[/tex].

To know more about Circle click the link given below.

https://brainly.com/question/20908820

I have $67 and spent $13 on ice cream, how much money do I have now?
$80
O $54

Answers

Answer:

Step-by-step explanation:

54

Graph the following equation Y=3/4x-2

Answers

Your first point is your y-intercept, which is -2. That means you plot a point at (0,-2).

From that point rise 3 and run (to the right) 4. Plot your second point there.

Connect the two points.

which value is a solution to the inequality x<4

a)4
b)0
c)5
d)4.5​

Answers

Answer:

a) 4

Step-by-step explanation:

B) 0

Since that the sign given is "less than", we will have the lower digit than 4. Since 0 is the only number less than 4, it is the answer.

[tex] = \tt{\green{\boxed{\tt{{0}}}} \: < \: 4}[/tex]

0 is less than 4.

Martha was recarpeting her bedroom, which was 15 feet long and 10 feet wide. How many square feet (the area) will she need to purchase?

Answers

Answer:

150 Square feet

Step-by-step explanation:

15 feet long

10 feet wide

Area = length x width

15 x 10 = 150

150 Square feet

Hope this helped!

what 2 fun facts did you learn about the inauguration

Answers

1-there were a huge amount of firsts yesterday
2-first ever inauguration the ex president didn’t go

David saw 30 birds in one day how many sparrow did he see

Answers

Answer:

15

Step-by-step explanation:

cause half of 30 is 15 super easy

Answer:

15

Step-by-step explanation:

I used my calculator and it gave me that awnser

A bookstore had 45 copies of a magazine. Yesterday, it sold 2/3 of them. Today, it sold 3/5 of what remained. How many copies does the bookstore have left?

Answers

The bookstore has 10 copies left.

Step- By- Step Explanation

After the first day, 1/3 of the original amount remained: (1/3)·45 = 15

After the second day, 2/3 of that amount remained: (2/3)·15 = 10

Four students can choose to participate in a charity event either on Saturday or Sunday. What’s the probability that there is at least one student at both Saturday's and Sunday's events?
A. 1/8

B. 3/8

C. 5/8

D. 7/8

Answers

Answer:7/8

Step-by-step explanation:edededededededededededed

Question 9
Find the length of
ST
s
T T
5
U

Answers

Answer:

5

Step-by-step explanation:

The answer is 5 because all angles are congruent.

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