an eight foot ladder leans against a building. if the ladder makes an angle of 60° with the ground, how far up the wall does the ladder reach?
Answers
Answer:
The ladder reaches (4)(√3) ft up the wall (6.93 ft)
Step-by-step explanation:
Think of a triangle with a 60 degree angle in the lower left corner. The lower right corner is a right triangle, and 8 ft is the length of the hypotenuse. The other angle is 30 degrees.
We know the angle 60 degrees, plus the length of the hypotenuse, but need the length of the vertical side opposite the 60 degree angle. Use the sine function here because it involves these knowns:
opposite side
sin 60 degrees = ------------------------ = x/(8 ft) = (√3)/2
Cross-multiplying, we get:
2x = (8 ft)(√3), or through reduction, x = (4)(√3)
The ladder reaches (4)(√3) ft up the wall (6.93 ft)
With the ground, [tex]6.92 ft[/tex] the wall does the ladder reach.
What is right angled triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle.
According to the question
An eight foot ladder leans against a building. if the ladder makes an angle of 60° with the ground.
From the right angle triangle,
[tex]sin 60^{0} =\frac{h}{8}[/tex]
[tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{h}{8}[/tex]
[tex]8\sqrt{3} =2h[/tex]
[tex]h = 4\sqrt{3}[/tex]
[tex]h = 6.92 ft[/tex]
Hence, With the ground, [tex]6.92 ft[/tex] the wall does the ladder reach.
Find out more information about right angle triangle here
https://brainly.com/question/3772264
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Related Questions
Which of the following statements are not true about parallelograms?
Select all that apply.
1. The area of a parallelogram is half of the product of its length and width.
2. The angles formed by the diagonals of a parallelogram are complementary to each
other.
3. The diagonals of a parallelogram bisect each other.
4. A diagonal divides a parallelogram into two congruent triangles.
5. Two consecutive angles of a parallelogram are supplementary.
Answers
9514 1404 393
Answer:
1, 2
Step-by-step explanation:
1. The area of a parallelogram is the product of length and width. The given statement is FALSE.
2. The angles formed by the diagonals are linear pairs, so supplementary. The given statement is FALSE.
3. TRUE
4. TRUE
5. TRUE
__
Statements 1 and 2 are not true.
A person is walking at a rate of 9 feet every 4 seconds.
(a) Find their speed, i.e. the rate the distance
Answers
Answer:
v = 2.25 ft/s
Step-by-step explanation:
Given that,
A person is walking at a rate of 9 feet every 4 seconds.
We need to find their speed. We know that, the speed of total distance divided by time taken. So,
[tex]v=\dfrac{d}{t}\\\\v=\dfrac{9\ ft}{4\ s}\\\\v=2.25\ ft/s[/tex]
So, the speed is 2.25 ft/s.
William receives a weekly allowance according to the following formula: For each day that he remembers to do his chores, he eams 51.50, and for each day that he doesn't remember to do his chores, he loses
50.25. What amount of allowance would William receive for a week in which he remembers to do his chores on five days and forgets to do them on two days?
Answers
50.25 * 5 = 251.25
50.25 * 2= 100.5
251.25-100.5= 150.75
In a right triangle, if the hypotenuse is equal to 16 feet and the side adjacent to ∠θ is equal to 5 feet, what is the approximate measurement of ∠θ?
A. 18°
B. 75°
C. 15°
D. 72°
Answers
Answer:
D. 72°
Step-by-step explanation:
Given
Adjacent = 5feet
Hypotenuse = 16feet
Using SOH CAH TOA
cos theta = adj/hyp
cos theta = 5/16
cos theta = 0.3125
theta = arccos 0.3125
theta = 71.7
theta = 72 degrees
Crusaders attacked the city of Zara to rid it of Muslim influence tr
ue or false
Answers
Answer:
true
Step-by-step explanation:
1. Solve the formula h = 42t + 1/2at^2 for a
2. Solve the formula P = 2L + 2W for L.
Answers
Answer:
1) a = (2h-84t) / t²
2) L = (P-2W) / 2
Step-by-step explanation:
Formula #1:
step 1: subtract 42t
1/2at² = h - 42t
step 2: multiply by 2
at² = 2h - 84t
step 3: divide by t²
a = (2h - 84t) / t²
Formula #2:
step 1: subtract 2W
P - 2W = 2L
step 2: divide by 2
L = (P-2W) / 2
is 0.3 greater than 0.38
Answers
Answer:
No
Step-by-step explanation:
Because 0.38 is 0.08 more than 0.3.
Set up a proportion and use it to solve for x.
14
х
6
9
Answers
Answer:
x=21
Step-by-step explanation:
x/x+14=9/15
15x=9x+126
6x=126
x=21
Por favor si alguien sabe pliss
(escriba si o no)
Answers
Answer:
Respuesta: SI
Step-by-step explanation:
Números Racionales
Un número pertenece al conjunto de los números racionales (Q) si se puede expresar como una fracción de denominador diferente de cero, es decir, x es racional si:
[tex]\displaystyle x=\frac{a}{b}[/tex]
Donde a y b son número enteros y además b es diferente de cero
el número
[tex]\displaystyle -\frac{3}{5}[/tex]
Tiene un numerador igual a 3 y un denominador igual a 5 (independientemente del signo), por lo tanto cumple con las dos condicines y es efectivamente un número racional.
Respuesta: SI
A new car is purchased for 20700 dollars. The value of the car depreciates at 11% per year. What will the value of the car be, to the nearest cent, after 11 years?
Answers
Answer:
The answer for that is 5744.61
Sylvia set a goal of saving at least $200 in a savings account.
She currently has $60 in the account. If she invests $5 of her weekly allowance per
week, how many weeks will it take her to reach her goal?
Define the variable.
Answers
Answer:
twenty eight more weeks till$200
PLEASE HELP !!! ILL GIVE BRAINLIEST!! *DONT SKIP* ILL GIVE 40 POINTS.
Answers
Answer:
5.5
Step-by-step explanation:
Math help!! Answers to 7,8,9?
Answers
Answer:
7 is D which is 18.4...
8 is C: 42
9: C: 8.9
Step-by-step explanation:
hope it helps...
The ratio of boys to girls in a school is 5:6. Find the total number of children in the school if there are 6000 girls. Pls help
Answers
Answer:
11,000
Step-by-step explanation:
There are 5000 boys and 6000 girls.
5000 + 6000 = 11,000
Answer:
11,000
Step-by-step explanation:
Boys is 6000 so 6000+5000=11000
Identify a secant that contains a diameter of M
Answers
Explanation:
A secant is a line that touches two points on the circles edge. Unlike a chord, a secant will go beyond the circles edge. By that definition, AD and AM are eliminated. The secant must also go through the point M since that is the midpoint. The diameter always goes through the midpoint. AB doesn’t go through M. However, AC does successfully meet all the requirements. It has two points on the circle, the line goes farther than the circles edge, and the line passes through the point M.
Answer:
A. AC
Step-by-step explanation:
Help!!! Find c.
Round to the nearest tenth:
Answers
Answer:
[tex]c = 14.9cm[/tex]
Step-by-step explanation:
Given
[tex]b = 10cm[/tex]
[tex]B = 12^{\circ}[/tex]
[tex]A = 150^{\circ}[/tex]
Required
Determine the length of c
First, we calculate C (the third angle of the triangle).
[tex]C = 180 - A - B[/tex]
[tex]C = 180 - 150 - 12[/tex]
[tex]C = 18^{\circ}[/tex]
Using Sine's law, we make use of:
[tex]\frac{sin\ B}{b} = \frac{sin C}{c}[/tex]
By substituting values, we have:
[tex]\frac{sin\ 12}{10} = \frac{sin 18}{c}[/tex]
Cross multiply
[tex]c* sin\ 12 = 10 * sin\ 18[/tex]
Make c the subject
[tex]c = \frac{10 * sin\ 18}{sin\ 12}[/tex]
[tex]c = \frac{10 * 0.3090}{0.2079}[/tex]
[tex]c = 14.9cm[/tex] approximated
Runner A had a minor accident and is now 0.25 miles behind Runner B.
Runner B is currently has a speed of 7 miles per hour.
Runner A attempts to catch up runner B by running 8.5 miles per hour.
How long will it take Runner A to catch up to Runner B?
Answers
Answer:
It will take one sixth of a hour, that is, 10 minutes for Runner A to catch up to Runner B.
Step-by-step explanation:
Runner A is 0.25 miles behind Runner B.
Runner B has a speed of 7mph, while Runner A has a speed of 8.5 mph.
This means that each hour, Runner A catches up at a speed of 8.5 - 7 = 1.5 mph.
How long will it take Runner A to catch up to Runner B?
1 hour - 1.5 miles
x hours - 0.25 miles
[tex]1.5x = 0.25[/tex]
[tex]x = \frac{0.25}{1.5}[/tex]
[tex]x = \frac{1}{6}[/tex]
It will take one sixth of a hour, that is, 10 minutes for Runner A to catch up to Runner B.
Answer the attachment please
And subscribe to Offxcial Prxmiise
X=8 and y=3
Answers
Answer:
73
Step-by-step explanation:
8^2+3^2=64+9=73
Type the missing number that makes these fractions equal:
6
4.
8
Submit
Answers
Explain how you could find the difference of 1 and 0.1978.
Answers
Answer:
0.8022
Step-by-step explanation:
difference=subtraction
so we take 1 - 0.1978 and it equals 0.8022
Alberto left the airport and traveled toward the capital. One hour later Danielle left traveling 10 km/h faster in an effort to catch up to him. After five hours Danielle finally caught up. What was Alberto's average speed?
Answers
Answer:
Step-by-step explanation:
Alberto traveled v km/h.
After 1 hour they are v km apart.
Danielle travels (v+10) km/h.
The distance between them decreases by 10 km/h.
They meet in 5 hours, after Danielle has traveled 5v+50 km and Alberto has traveled 6v km.
6v = 5v+50
v = 50 km/h
Alberto travels 50 km/h
Use basic facts and place value to find the quotient.
450 • 9 =
Your answer
Answers
Select the ordered pairs that are solutions to the system of inequalities {y≤-2x+6x−y<6.
Select all that apply.
Answers
Answer:
(1.5, 0)
Step-by-step explanation:
Given the system of inequalities y≤-2x+6x−y<6.
separating the inequality
y≤-2x+6x−y
Get the y intercept. This occurs at x = 0
y≤-2(0)+6(0)−y
y = - y
y+y = 0
2y = 0
y = 0
Get the x intercept. This occurs at y = 0
-2x+6x−y<6
-2x+6x−0<6
4x < 6
x < 6/4
x < 3/2
x < 1.5
Hence the ordered pair is (1.5, 0)
Guys Please help
Tyra has 1223 cups of sugar. If r is the amount of sugar called for in one batch of cookies,
the expression 1223 ÷ r can be used to find how many batches Tyra can make with the sugar she has
If r is 23 cup, how many batches of cookies can Tyra bake
Answers
Answer:
53 cookies
Step-by-step explanation:
you divide 1223 and 23, the answer should then be about 53
what is a bar diagram
Answers
Answer:
A bar graph shows amounts as bars of different sizes and, sometimes, of different colors. Longer bars represent larger numbers.
The Anderson's are driving 2,563 miles to the beach. They plan to drive 325 miles a day. How many days will it take the Anderson's to drive to the beach?
Answers
Answer:
Around 8 days
Step-by-step explanation:
Divide 325 from 2,563
2563 / 325 = 7.888
Round that number
Find the degree measure of the indicated angle.
?
43°
75°
Answers
if x+y=z which property is used?
Answers
Answer:
addition
Step-by-step explanation:
Answer:
Addition??
Yeah maybe in what terms?
.3x+.65 x 175=.50(x+175)
Can you please explain this step by step? Kinda confused about how to figure it out.
Answers
Answer:
[tex]x=131.25[/tex]
Step-by-step explanation:
[tex]0.3x+0.65*175=0.5(x+175)[/tex]
[tex]0.3x+113.75=0.5x+87.5[/tex] (Simplify both sides of the equation by multiplying on the LHS and distributing on the RHS)
[tex]0.3x+113.75-0.5x=0.5x+87.5-0.5x[/tex] (Subtract [tex]0.5x[/tex] from both sides of the equation to get all [tex]x[/tex] terms to one side)
[tex]-0.2x+113.75=87.5[/tex] (Simplify)
[tex]-0.2x+113.75-113.75=87.5-113.75[/tex] (Subtract [tex]113.75[/tex] from both sides of the equation to isolate [tex]x[/tex])
[tex]-0.2x=-26.25[/tex] (Simplify)
[tex]\frac{-0.2x}{-0.2} =\frac{-26.25}{-0.2}[/tex] (Divide both sides of the equation by [tex]-0.2[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]x=131.25[/tex] (Simplify)
Hope this helps!
Write the function whose graph is the graph of y=√x, but is shifted to the left 7 units .
Answers
Answer:2x + 7 = 15
Step-by-step explanation:
2x + 7 = 15