Throughout this question, take care to explain your reasoning carefully. You should round your answers, where necessary, to two significant figures. Finn is looking into the position and range of 4G mobile towers in his local area. Finn learns that the range of the 4G mobile towers is 50 km, where there are no obstructions. (a) Calculate what area is within the range of a 4G mobile tower where there are no obstructions. (b) Finn looks at a map of 4G mobile towers in his area. There is one at Hollingworth Hill and another at Cleggswood Hill. The top of these towers have heights of 248 m and 264 m respectively. Let point A be the top of the tower at Hollingworth Hil, point B be the point vertically beneath Cleggswood tower and on a level with the point A and let point C be the top of the tower at Cleggswood Hill. A measurement of 4 cm on the map represents 1 km on the ground. (i) The horizontal distance between the two locations on the map is 3.5 cm. What is the actual horizontal distance between the masts (the length AB)? (ii) What is the reduction scale factor? Give your answer in standard form. (iii) What is the actual distance between the tops of the two towers, the length AC? (iv) Calculate ZCAB, the angle which is the line of sight from the top of the mast at Hollingworth Hill to the top of the mast at Cleggswood Hill?
Throughout this question, take care to explain your reasoning carefully. You should round your answers, where necessary, to two significant figures. Finn is looking into the position and range of 4G mobile towers in his local area. Finn learns that the range of the 4G mobile towers is 50 km, where there are no obstructions. (a) Calculate what area is within the range of a 4G mobile tower where there are no obstructions. (b) Finn looks at a map of 4G mobile towers in his area. There is one at Hollingworth Hill and another at Cleggswood Hill. The top of these towers have heights of 248 m and 264 m respectively. Let point A be the top of the tower at Hollingworth Hil, point B be the point vertically beneath Cleggswood tower and on a level with the point A and let point C be the top of the tower at Cleggswood Hill. A measurement of 4 cm on the map represents 1 km on the ground. (i) The horizontal distance between the two locations on the map is 3.5 cm. What is the actual horizontal distance between the masts (the length AB)? (ii) What is the reduction scale factor? Give your answer in standard form. (iii) What is the actual distance between the tops of the two towers, the length AC? (iv) Calculate ZCAB, the angle which is the line of sight from the top of the mast at Hollingworth Hill to the top of the mast at Cleggswood Hill?
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter7: Locus And Concurrence
Section7.2: Concurrence Of Lines
Problem 42E: There are plans to locate a disaster response agency in an area that is prone to tornadic activity....
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Transcribed Image Text:Throughout this question, take care to explain your reasoning carefully. You
should round your answers, where necessary, to two significant figures.
Finn is looking into the position and range of 4G mobile towers in his local
area. Finn learns that the range of the 4G mobile towers is 50 km, where
there are no obstructions.
(a) Calculate what area is within the range of a 4G mobile tower where
there are no obstructions.
(b) Finn looks at a map of 4G mobile towers in his area. There is one at
Hollingworth Hill and another at Cleggswood Hill. The top of these
towers have heights of 248 m and 264 m respectively. Let point A be the
top of the tower at Hollingworth Hill, point B be the point vertically
beneath Cleggswood tower and on a level with the point A and let
point C be the top of the tower at Cleggswood Hill. A measurement of
4 cm on the map represents 1 km on the ground.
(i) The horizontal distance between the two locations on the map is
3.5 cm. What is the actual horizontal distance between the masts
(the length AB)?
(ii) What is the reduction scale factor? Give your answer in standard
form.
(iii) What is the actual distance between the tops of the two towers, the
length AC?
(iv) Calculate 2CAB, the angle which is the line of sight from the top
of the mast at Hollingworth Hill to the top of the mast at
Cleggswood Hill?
(c) A third tower is located at Heights Barn Hill. Let DEF represent the
points on the map for Cleggswood Hill, Hollingworth Hill and Heights
Barn Hill respectively. On the map, DE = 3.5 cm and EF = 5.5 cm and
ZDEF = 105°.
(i) Is ZDEF on the map greater than, less than, or the same as the
angle between the horizontal line between Cleggswood Hill and
Hollingworth Hill and the horizontal line between Hollingworth Hill
and Heights Barn Hill in real life? Explain your answer.
(ii) Find the length DF.
(iii) Find the EFD.
(iv) Find the area of triangle DEF.
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(c) A third tower is located at Heights Barn Hill. Let DEF represent the points on the map for Cleggswood Hill, Hollingworth Hill and Heights Barn Hill respectively. On the map, DE = 3.5 cm and EF = 5.5 cm and ∠DEF = 105◦
Solution
by Bartleby ExpertFollow-up Question
(c) A third tower is located at Heights Barn Hill. Let DEF represent the points on the map for Cleggswood Hill, Hollingworth Hill and Heights Barn Hill respectively. On the map, DE = 3.5 cm and EF = 5.5 cm and ZDEF = 105°.
(i) Is ZDEF on the map greater than, less than, or the same as the angle between the horizontal line between Cleggswood Hill and Hollingworth Hill and the horizontal line between Hollingworth Hill and Heights Barn Hill in real life? Explain your answer.
(ii) Find the length DF.
(iii) Find the EFD.
(iv) Find the area of triangle DEF.
Solution
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