The entrance to a horizontal mining tunnel has collapsed, trapping the miners inside.The rescue team decide to drill a vertical escape shaft from a position 200 m further
up the hill. If the hill slopes at 23◦ from the horizontal, how deep does the rescue shaft
need to be to meet the horizontal tunnel? Answer to one decimal place.
Answers
Answer: 78.1 meters
Explanation
The diagram is shown below.
We have a right triangle with an unknown vertical leg (which I'll call x) and a known hypotenuse that is 200 meters long.
We use the sine ratio to connect the opposite and hypotenuse.
sin(angle) = opposite/hypotenuse
sin(23) = x/200
x = 200*sin(23)
x = 78.1462256978548 approximately
x = 78.1
Make sure your calculator is in degree mode.
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Answers
So, the measure of angle EAF would also be x.
Now, the sum of the angles in a triangle is always 180 degrees.
From the given diagram, we have:
Angle T = 100 degrees
Angle EAF = x degrees
Angle A = 90 degrees
To find the two angle measures not given in the diagram, we can use the fact that the sum of angles in a triangle is 180 degrees.
180 = Angle T + Angle EAF + Angle A
Substituting the given angle measures:
180 = 100 + x + 90
Simplifying the equation:
180 = 190 + x
Next, we solve for x:
x = 180 - 190
x = -10
We found that x is equal to -10. However, in the context of angles, negative values are not meaningful. Therefore, we can conclude that there is no unique solution for the two angle measures not given in the diagram.
Answers
Answer:
15/2, 13/2.
Step-by-step explanation:
Here's a graph as well.
Answer in fraction form = (15/2, 13/2)
Answer in decimal form = (7.5, 6.5)
========================================================
Explanation:
To get the midpoint, we average the two endpoint values. We handle the x and y coordinates separately.
The x coordinates of each point are 6 and 9. They average to (6+9)/2 = 15/2 = 7.5; so you add up the x coordinates and divide by 2.
The y coordinates are handled the same way. Add them to get 4+9 = 13 and then divide by 2 to get 13/2 = 6.5
The midpoint is (15/2, 13/2) = (7.5, 6.5)
Answers
−9.8−4.3
Yes
No
−9.8+(−0.2)+(−4.1)
Yes
No
−9.8−0.2+4.1
Yes
No
−9.8+(−0.2−4.5)
Yes
No
−9.8+0.2−4.5
Yes
No
Answers
b=yes
c=no
d=no
e=yes
Answer:
^^^^
Step-by-step explanation:
Answers
Answer:
U (1, 16 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ), then the midpoint M is
M = ( ,
) ← midpoint formula
let (x₁, x₂ ) = U (x, y ) and (x₂, y₂ ) = V (13, 8 )
substitute these values into the midpoint formula and equate to the corresponding coordinates of M (7, 12 )
= 7 ( multiply both sides by 2 )
x + 13 = 2 × 7 = 14 ( subtract 13 from both sides )
x = 1
and
= 12 ( multiply both sides by 2 )
y + 8 = 2 × 12 = 24 ( subtract 8 from both sides )
y = 16
coordinates of U = (1, 16 )
Answers
4 * 4 (or
16 * 4 *4 *4 *4 *4
16384 people will know the art of quilling