The height of a radio tower is 400 feet, and the ground on one side of the tower slopes upward at an angle of 10degrees. (a) H
ow long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 190 feet from the base of the tower? (b) How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a point 190 feet from the base on the flat side?
1 answer:
Answer:
(a) 412 ft
(b) 276 ft
Step-by-step explanation:
Consider the attached diagram.
(a) The internal angle of triangle RBT at B is 90° -10° = 80°. Since we know lengths RB and BT, we can find the length RT using the law of cosines:
RT² = RB² +BT² -2·RB·BT·cos(80°) = 190² +400² -2·190·400·cos(80°)
RT² ≈ 169,705.477
RT ≈ √169,705.477 ≈ 411.95
The guy wire to the hillside should be about 412 feet long.
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(b) The Pythagorean theorem can be used to find the shorter wire length.
LM² = LB² +MB²
LM = √(190² +200²) = √76,100
LM ≈ 275.86
The guy wire to the flat side should be about 276 feet long.
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Step-by-step explanation:
The box-and-whisker plot is attached.
We first order the data from least to greatest:
67,68,68,69,70,72,73,74,75,75,76,78,79,79,80,83,84,85,85,88
Now we find the median. Since there are 20 data values, the median is between 75 and 76:
(75+76)/2 = 151/2 = 75.5
Now we find the Lower Quartile (LQ). We do this by finding the median of the lower half of data (from the median down). There are 10 values here; the median is between 70 and 72:
(70+72)/2 = 142/2 = 71
Find the Upper Quartile (UQ). Do this by finding the median of the upper half of data (from the median up). There are 10 values here; the median is between 80 and 83:
(80+83)/2 = 163/2 = 81.5
The middle bar of the box is over the median. The left hand side of the box is over LQ, and the right hand side of the box is over UQ. Now we draw a whisker from the box to the highest value, 88, and from the box to the lowest value, 67.
We first order the data from least to greatest:
67,68,68,69,70,72,73,74,75,75,76,78,79,79,80,83,84,85,85,88
Now we find the median. Since there are 20 data values, the median is between 75 and 76:
(75+76)/2 = 151/2 = 75.5
Now we find the Lower Quartile (LQ). We do this by finding the median of the lower half of data (from the median down). There are 10 values here; the median is between 70 and 72:
(70+72)/2 = 142/2 = 71
Find the Upper Quartile (UQ). Do this by finding the median of the upper half of data (from the median up). There are 10 values here; the median is between 80 and 83:
(80+83)/2 = 163/2 = 81.5
The middle bar of the box is over the median. The left hand side of the box is over LQ, and the right hand side of the box is over UQ. Now we draw a whisker from the box to the highest value, 88, and from the box to the lowest value, 67.