A park is showing a movie on the lawn. The base of the screen is 6 feet off the ground and the screen is 22 feet high (see figure).
Answer:
A. 61.82°;
15.64°
B. 33.37°
Step-by-step explanation:
A.
✍️Angle of elevation from 15 ft:
A right triangle is formed. Apply trigonometric ratios formula to find the angle of elevation from 15 ft.
Thus,
Length of the side Opposite to reference angle = 22 + 6 = 28 ft
Adjacent length = 15 ft
Thus, we would have:
[tex] tan(\theta) = \frac{opp}{adjacent} = \frac{28}{15} [/tex]
[tex] tan(\theta) = 1.8667 [/tex]
[tex] \theta = tan^{-1}(1.8667) [/tex]
[tex] \theta = 61.82 [/tex] (2 d.p)
✍️Angle of elevation from 100 ft:
Thus,
Length of the side Opposite to reference angle = 22 + 6 = 28 ft
Adjacent length = 100 ft
Thus, we would have:
[tex] tan(\theta) = \frac{opp}{adjacent} = \frac{28}{100} [/tex]
[tex] tan(\theta) = 0.28 [/tex]
[tex] \theta = tan^{-1}(0.28) [/tex]
[tex] \theta = 15.64 [/tex] (2 d.p)
B.
✍️Distance you'd be from the screen if you lie on the ground and make an angle of elevation of 40° to the top of the screen:
Adjacent length = your distance from the screen = x
Opposite length = 22 + 6 = 28 ft
Angle of elevation = 40°
Tge trigonometric ratios formula to use would be:
[tex] tan(\theta) = \frac{opp}{adjacent} [/tex]
Plug in the values
[tex] tan(40) = \frac{28}{x} [/tex]
Multiply both sides by x
[tex] x*tan(40) = 28 [/tex]
Divide both sides by tan(40)
[tex] x = \frac{28}{tan(40)} [/tex]
[tex] x = 33.37 [/tex] (2 d.p)
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Answer:
Step-by-step explanation:
15 5/12 minus 11 1/8 A. 4 7/24 B. 4 7/12 C. -4 1/3 D.-4 7/24
Answer:
A. 4 7/24
Step-by-step explanation:
subtract 15 - 11 which equals 4
then do 5/15 - 1/8 =7/24
Does the system have a no solution or infinitely many solutions
Y=2/3x+2-2x+3y=6
Answer:
answer for y=2/3x+2: y=2/3x+2
answer for -2x+3y=6: x=3/2y-3
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Answer:
There are infinitely many solutions.
Step-by-step explanation:
There are infinitely many solutions because if you solve the equations, you will find that both of the equations are actually the same, so there is infinitely many solutions.
Showing that both equations are equal: y=2/3x+2 -2x+3y=6
y=2/3x+2 Multiply by 3 on both sides
3y=2x+6 Rearrange (-2x on both sides)
3y-2x=6 More rearrangement
-2x+3y=6 Now, if you look back at the second equation, you will see that they are both the same.
If a roof is 24 feet high and if you leaned a 26 foot ladder against the side of a building how far away from the building is the base of a ladder to reach the roof
Answer: 35.4 feet.
Step-by-step explanation:
Given data:
Height of the roof = 24 feet
Height of the ladder = 26 foot
Solution:
c^2 = a^2 + b^2
a = 24
b = 26
c^2 = 24^2 + 26^2
c = √576 + 676
c = √1252
c = 35.4 feet
The foot of the ladder is 35.4 foot away from the top of the ladder.
Answer:
The distance between the base of the ladder and the building is 10 ft
Step-by-step explanation:
Here, we want to calculate the distance between the foot of the ladder and the building
To get this, we need to have a pictorial representation. Please check the attachment for this
From the pictorial representation, we can see a right angled triangle with a hypotenuse of 26 feet and the other side being 24 feet. We now need to get the third side of this triangle which represents the distance we want.
Mathematically, we can calculate the distance using Pythagoras’ theorem which states that the square of the length of the hypotenuse is equal the sum of the squares of the two other sides of the triangle.
Let the distance we are looking for be D
26^2 = 24^2 + D^2
D^2 = 26^2 - 24^2
D^2 = 100
D^2 = 10^2
D = 10 feet
What is 6.5% of 39.99?
My Fav Football team what’s yours? Follow and Like
Answer:
I don't like Football...
Step-by-step explanation:
Answer: My fav is the New York Giants
Step-by-step explanation:
please help, my time is running out
Answer: 40 ?
Step-by-step explanation:
If x = -2, what is the value of y, that makes the equation, y = 2x + 3, true? Explain how you know.
Answer:
Y is equals to negative 1.
Step-by-step explanation:
y = 2x + 3
y =2(-2)+ 3
y =-4+ 3
y=-1
Average ant weight 4x10^-3 grams. Ant population is 10,000 trillion (10,000,000,000,000,000). What is the total mass of all ants? Show work for mass of ants (grams):
Answer:
The total mass is 4 * 10^12 grams
Step-by-step explanation:
To get the total mass of all ants,
We simply multiply the average mass of an ant by the population
That will be;
4 * 10^-3 * 10^15
= 4 * 10^12 grams
what is the equation of the line that passes through the point (4,-5) and is parallel to the line y=1/2x+5
Answer:
y=1/2x - 7
Step-by-step explanation:
Since the lines are parallel, this means that the slopes will be the same, only the y-intercept will change. I graphed this out to find the answer.
Write an equation in slope-intercept form of the line with slope −6/5 that contains the point (−5,3)
Answer:
y=-6/5x-3
Step-by-step explanation:
y-3=-6/5(x+5)
y=-6/5x-3
Eddie deposits $1090 in an account that earns 6% interest compounded annually for 3 years. What is the total interest earned after 3 years? Round to the nearest cent.
A: 196.20
B: 208.20
C: 1286.20
D: 1298.20
Answer:
Step-by-step explanation:
Eddie deposits $1090 in an account that earns 6% interest compounded annually for 3 years. What is the total interest earned after 3 years? Round to the nearest cent.
A: 196.20
B: 208.20
C: 1286.20
D: 1298.20