Answer: x= 19.5
(4x+12) = 90
Step-by-step explanation:
Notice the denoted right angle at the very top left. This means those intersecting lines are perpendicular forming 90 degree angles. All right angles are equal in measure so all 4 angles at the top are 90 degrees. We can then use corresponding angles to know that all of the bottom 4 angles are also 90 degrees. Now we can solve for x. (4x+12) =90. 4x= 78. X= 19.5
We should find the area of the carpet squares. Since each side is 1 foot, the area will be 1. Now, Julie used 120 carpet squares, which is 1 in area. So, we will have to multiply 1 by 120.
120×1=120
The area of the floor is 120 ft².
<h3>
Answer: Approximately 119.76 meters</h3>
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Work Shown:
x = starting length of the shadow
y = height of the pole
tan(angle) = opposite/adjacent
tan(58) = y/x
1.6003345 = y/x
1.6003345x = y
x = y/1.6003345
x = (1/1.6003345)y
x = 0.62486936y
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When the angle changes, the adjacent side gets 90 meters longer
tan(angle) = opposite/adjacent
tan(36) = y/(x+90)
0.72654253 = y/(0.62486936y+90)
0.72654253(0.62486936y+90) = y
0.453994166y + 65.3888277 = y
65.3888277 = y-0.453994166y
65.3888277 = 0.546005834y
0.546005834y = 65.3888277
y = 65.3888277/0.546005834
y = 119.758478075162
y = 119.76
The height of the pole is about 119.76 meters.
Answer: B . Converse of the alternate exterior angle theorem.
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