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oksano4ka [1.4K]
3 years ago
15

If a ladder is to be placed 3 feet from the side of a house. If top of the ladder rests exactly on the edge of the house when it

is placed at an angle of 72 degrees from the ground, how long is the ladder to the nearest foot?
Mathematics
1 answer:
likoan [24]3 years ago
6 0

Answer:

7 feet long

Step-by-step explanation:

This set up will give a right angle triangle where;

Length of the ladder is the hypotenuse = x

The distance of the ladder to the house is the adjacent = 3 feet

Angle of elevation theta = 72 degrees

Using the CAH in trigonometry identity;

cos theta = adjacent/hypotenuse

cos 72 = 3/hyp

hyp = 3/cos72

hyp = 3/0.4258

hyp = 7.05 feet

Hence the ladder is approximately 7 feet long

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Two angles are supplementary. Which of the following equations can be used to find the value of the missing angle, x, if the oth
Natali [406]

Two angles are said to be supplementary if their sum is 180 degrees. So, if x and y are supplementary angles, the formula is

x + y = 180

We know that one of the angles (say x) is 98. So, the equation updates to

98 + y = 180

If we want to solve for the other angle, we can simply subtract 98 from both sides to get

y = 180-98 = 82

6 0
3 years ago
HELP IM IN DESPERATE NEED!!!<br> What is the solution to this system of equations?
Paladinen [302]

[Given]

{ x + y = 6

{ x = y + 4

[Plug-in our x value & solve]

[Given] x + y = 6

[ Plug-in] (y + 4) + y = 6

[Distribute] y + 4 + y = 6

[Combine like terms] 2y + 4 = 6

[Subtract 4 from both sides] 2y = 2

[Divide both sides by 2] y = 1

[Answer]

Third option - (5, 1)

-> You do not need to solve for x since this is the only option that has y = 1, but to solve for x we would do y + 4 = 1 + 4 = 5, so this answer fully checks correctly

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

     ★ Also please leave the rating you think I deserve (It helps other users as well as myself)

- Heather

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2 years ago
A bag contains 5 blue, 3 red, 6 green, 9 orange, and 20 black marbles. What is the ratio of the number of blue marbles to the nu
barxatty [35]

Answer:

C

Step-by-step explanation:

blue+green=15

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5 to 15

4 0
3 years ago
Read 2 more answers
Lexi needs 144 beads. A large box holds 100 beads. A medium box holds 10 beads. A small box holds 1 bead. Lexi already had 1 lar
ohaa [14]
She has 144-100=44.  44-4=40.  Medium holds to beads you will need 4 medium boxes.
7 0
3 years ago
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What is the zero in the quadratic function f(x)= 9x^2-54x-19?
Alex17521 [72]

Answer:

6.33... and 0.333...

Step-by-step explanation:

The quadratic formula is


x=\frac{-b+\sqrt{b^2-4ac} }{2a}.


It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions.  Using the formula will require less work than finding the factors if factorable. We will substitute a=9, b=-54 and c=-19.

x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-(-54)+/-\sqrt{(-54)^2-4(9)(-19)} }{2(9)}\\x=\frac{54+/-\sqrt{2916+684} }{18}

We will now solve for the plus and the minus.

The plus,,,

x=\frac{54+\sqrt{3600}}{18}\\x=\frac{54+60}{18}\\x=\frac{114}{18}\\x=6.3

and the minus...

x=\frac{54-\sqrt{3600}}{18}\\x=\frac{54-60}{18}\\x=\frac{-6}{18}\\x=-0.333...

8 0
3 years ago
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