# Heights and Distances Questions and Answers

Math

Heights and DistancesStarla is 5 feet 9 inches tall. To find
the height of a tree, she measured her
shadow and the tree's shadow. Her
shadow was 8 feet long when the tree's
shadow was 30 feet long. To the nearest
foot, how tall is the tree?
F 15 ft
H 28 ft
G 22 ft
J 42 ft

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Heights and DistancesSelect all of the following types of measurements that are measures of 2-dimensions.
(2-dimensional measurements will have a units² attached to them. There may be more than one answer,
select all answers.)
Perimeter
Volume
Length
Surface Area
Area

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Heights and DistancesThe base of a 10-foot ladder is 2 feet from a building. If the ladder reaches the flat roof, how tall is the building?

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Heights and DistancesBrandon is on one side of a river that is 80 m wide and wants to reach a point 250 m downstream on the opposite side as quickly as possible by swimming diagonally across the river and then running the rest of the way. Find the minimum amount of time if Brandon can swim at 2 m/s and run at 4 m/s. (Use decimal notation. Give your answer to two decimal places.)

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Heights and DistancesThe angle of elevation from a boat to a hovering helicopter is 32.2° and the helicopter is 600 feet above the water level. What is the horizontal distance, to the nearest foot, between the boat and the helicopter?

Math

Heights and DistancesA helicopter is flying at an elevation of 320 feet.
It is within sight of the landing pad and the pilot finds that the angle of depression to the landing pad is 14°.
Find the distance between a point on the ground directly below the helicopter and the landing pad. Round your answer to the nearest foot.
Note that for this problem, we are using degrees to measure angles. Make sure your calculator is set to degrees instead of radians.

Math

Heights and DistancesOne bag of lawn fertilizer can cover approximately 5,000 square feet. Mike's lawn is
about 500 square feet. When Mike applies fertilizer to his lawn, he applies it to 3/4 of
his lawn only. About how many complete times can Mike fertilize his lawn with one
bag of fertilizer?
a) 13
b) 10
c) 1
d) 14

Math

Heights and DistancesA plane is flying at an elevation of 24000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 14°.
Find the diagonal distance between the plane and the base of the airport. Round your answer to the nearest foot. .
Note that for this problem, we are using degrees to measure angles. Make sure your calculator is set to degrees instead of radians.

Math

Heights and DistancesThe surface area of a small toy ball is 18 square inches. If the radius of the ball is tripled, what will be the surface area of the new, larger ball in square inches?
F 18 in.²
H 54 in.²
G 36 in.2
J 162 in.²

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Heights and Distances#8 An airplane is flying 700 feet above ground. From the plane to the base of the control tower, the angle of depression is 47°. How far away is ground directly underneath the plane to the control tower? Round your answer to the nearest tenth.

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Heights and DistancesYou are skiing down a mountain with a vertical height of 1000 feet. The distance from the top of the mountain to the base is 2000 feet. What is the angle of elevation from the base to the top of the mountain?

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Heights and DistancesTo estimate the height of a building, a student stood a certain distance from a building and determined that the angle of elevation to the top of the building was 32°. The student then moved 200 feet closer to the building along a level street and determined the angle of elevation was 42°. What is the height of the building?
315.3 feet
628.7 feet
116.5 feet
408.4 feet

Math

Heights and DistancesWhen comparing the volume of pyramids and prisms, what is the ratio of the volume of the pyramid to the volume of the prism If
the bases are the same?
1:2
1:4
1:6
1:3

Math

Heights and DistancesA company manufactures cylindrical containers that each have a volume of 6 cubic feet. For a new
container design, the company plans to keep the same height for the container and double the
radius.
Which statement best describes how this change will affect the volume of the container?
F The volume will be multiplied by a factor of 2.
H The volume will be multiplied by a factor of 0.5.
G The volume will be multiplied by a factor of 4.
JThe volume will be multiplied by a factor of 0.25.

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Heights and DistancesLighthouse Master Jack Simmons is atop his 300 ft lighthouse and spots a boat in the distance at an angle of depression of 18°. How far is the boat
from the lighthouse?
Round your answer to the nearest Hundredth
Distance =
Ift

Math

Heights and DistancesWhich of the following would not be a correct description of slope?
a. rise/run
b. The height that a line rises.
c. How gently or steeply something is slanted.
d. The change in vertical distance compared to the change in horizontal distance.

Math

Heights and DistancesYou approach a hill on top of which there is a tall radio antenna. You know from your map that your horizontal distance from the bottom of the radio antenna is 600 feet. The angle of elevation to the bottom of the antenna is 10°, and the angle of elevation to the top of the antenna is 25°. You figure that the height of the hill is feet, and the height of the antenna is feet. (Enter your answers rounded to the nearest foot.)
Hint: Draw a picture. Figure out the height of the hill. Figure out the combined height of the antenna and the hill. Compute the difference.

Math

Heights and DistancesA support wire for a telephone pole makes an angle of elevation of 65° with the ground. If the bottom of the wire is 18 ft from the pole, how tall is the pole? (Round your answer to the nearest thousandth)

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Heights and DistancesFireman Bob leans a 40 foot ladder against a building at an angle of elevation of 70°. How far is the base of the ladder from the building (round your answer to the nearest thousandth)?
Distance from base of the building =
ft

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Heights and DistancesA wheelchair ramp is 24 ft long and connects with a building 4 ft above the ground. What is the angle of elevation of the ramp?
Round your answer to the nearest WHOLE degree.
Angle of elevation =

Math

Heights and DistancesA kite string is being held 3 ft above the ground. The string is 185 ft long and is flying at an angle of elevation of 36°. Round your answer to the nearest tenth.
Height of the the kite =

Math

Heights and DistancesAn airplane is flying at an altitude of 12,600 feet above the ground. The angle of depression from the plane to the base of a tree is 15° 45'. How far horizontally must the plane fly in order to be directly over the tree?

Math

Heights and DistancesA wire is attached to the top of the tower and to a point on the ground that is 35 m from the base of the
tower. If the wire makes a 65° angle with the ground, how long is the wire?

Math

Heights and DistancesA rectangular picture frame has a length of 7 inches and a width of 5 inches.
What is the length of the diagonal of the picture frame?
8.2 inches
8.4 inches
8.6 inches
8.8 inches

Math

Heights and DistancesAllison kicks a stone off the edge of a tall cliff. The distance d (in feet), between the rock and the ground seconds after being kicked is d(t)= -t^2 +4t+474.
a. How many seconds elapse before the rock is at a height of 424 feet above the ground? Round your answer to the nearest tenth of a second.
b. What is the maximum height that the rock reaches? Round your answer to the nearest whole foot.

Math

Heights and DistancesTo get from point A to point B, you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
45 meters
34 meters
22 meters
53 meters

Math

Heights and DistancesA 10-ft-tall fence runs parallel to the wall of a house at a distance of 9 ft. Find the length of the shortest ladder that extends from the ground to the house without touching the fence. Assume the vertical wall of the house is 20 ft high and the horizontal ground extends 25 ft from the fence.
The length of the shortest ladder is

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Heights and DistancesAurelia needs to drive 280 miles. If she drives at a rate of 65 miles per hour, to the nearest tenth of an hour, how long will the trip take?

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Heights and DistancesAlice and Amy decide to meet at a party. From a corner of the party hall, Amy spots Alice at the corner of the hall diagonally opposite her. If the party hall is a rectangle that measures 100 feet by 60 feet, what is the shortest distance Amy has to walk to reach Alice? Round your answer to
the nearest foot.
A. 40 feet
B. 80 feet
C. 117 feet
D. 160 feet

Math

Heights and DistancesA boat leaves the marina and sails 5 miles west, then 10 miles southeast. How far, in miles, from the marina is the boat?
(Round your answer to the nearest hundredth if necessary.)

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Heights and DistancesThe density of gold is 19.3 g/cm³. A weight of 1 ounce is equivalent to a mass of about 28.35 g. Which of these is closest to the side length of a cube-shaped block of gold that has a weight of 8 ounces?
A. 2.27 cm
B. 3.43 cm
C. 9.09 cm

Math

Heights and DistancesCesar is making a model of the Eiffel Tower. The height of the tower is 984 feet, and Cesar wants to make a 1.5-foot model.
What scale should Cesar use? Find the scale in inches to feet. Round your answer to the nearest tenth of a foot.

Math

Heights and DistancesA cross section of a nuclear cooling tower is a hyperbola with equation
x² /90² - y² /130² - = 1.
The tower is 450 ft tall, and the distance from the top of the tower to the center of the hyperbola is half the distance from the base of the tower to the center of the hyperbola. Find the diameter of the top and the base of the tower.

Math

Heights and DistancesA small motorboat travels 15 mph in still water. It takes 2 hours longer to travel 69 miles going upstream than it does going downstream. Find the rate of the current. (Hint: 15 + x = rate going downstream and 15 - x = rate going upstream.)(Round your answer to the nearest tenth.)

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Heights and Distances➤ 4-19 When she was younger, Mary had to look up at a 68° angle to see into her father's eyes whenever she was standing 15 inches away. How high above the flat ground were her father's eyes if Mary's eyes were 32 inches above the ground?

Math

Heights and DistancesIn 2011, there were 3223 sea otters in Monterey Bay, California. The bay is
approximately 77 square miles. To the nearest whole number, what was the
density of the sea otter population?
A. 41.9 otters/mile2
B. 547.2 otters/mile²
C. .02 otters/mile²
D. 84.6 otters/mile²

Math

Heights and DistancesThe top of a 5 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 3 feet per second. How fast is the bottom of the ladder sliding along the ground away from the wall when the bottom of the ladder is 4 feet away from the base of the wall?

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Heights and DistancesLB. Johnson Middle School held a track and field event during the school year. The chess club sold various drink and snack items for the participants and the audience. Altogether, they sold 486 items that totaled $2,673.

Math

Heights and DistancesThe height above ground (in feet) of a ball dropped from the top of a tall building after t seconds is given by the polynomial h=-16t^2 +53. What is the height after 1 second? After 5/4 What is the height after 1 second?

Math

Heights and DistancesA ladybug crawls around the outside of a rectangle that measures 12 cm by 15 cm. The ladybug
stays exactly 1 cm from the rectangle at all times to form a larger figure.
How far does the ladybug crawl in one trip around the figure?
?
What is the area of the new rectangle bound by the path of the bug?
?

Math

Heights and DistancesCar A leaves Santa Barbara at noon traveling south toward Los Angeles at 60 mph. At 1pm car B leaves Los Angeles traveling north toward Santa Barbara at 85 mph. The distance between the cars at noon was 100 miles. If car B does not get pulled over, how many minutes after car B leaves will they pass each other?

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Heights and DistancesAn object is thrown upward at a speed of 52 feet per second by a machine from a height of 20 feet off the ground. The height h of the object after t seconds can be found using the equation h= 16t² +52t + 20

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Heights and DistancesA man standing 13 feet from the base of a lamppost casts a shadow 5 feet long. If the man is 6 feet tall and walks away from the lamppost at a speed of 400 feet per minute, at what rate, in feet per minute, will the length of his shadow be changing?

Math

Heights and DistancesA ball is thrown from an initial height of 1 meter with an initial upward velocity of 7 m/s. The ball's height h (in meters) after f seconds is given by the following.
h=1+71-57
Find all values off for which the ball's height is 2 meters.
Round your answer(s) to the nearest hundredth.

Math

Heights and DistancesA ball is thrown from a height of 217 feet with an initial downward velocity of 17 ft/s. The ball's height / (in feet) after t seconds is given by the following. How long after the ball is thrown does it hit the ground? Round your answer(s) to the nearest hundredth.

Math

Heights and DistancesTo measure a stone face carved on the side of a mountain, two sightings 850 feet from the base of the mountain are taken. If the angle of elevation to the bottom of the face is 26° and the angle of elevation to the top is 29°, what is the height of the stone face?

Math

Heights and DistancesA ball is thrown from an initial height of 3 meters with an initial upward velocity of 5 m/s. The ball's height / (in meters) after / seconds is given by the following.
h-3451-57
Find all values of f for which the ball's height is 4 meters.
Round your answer(s) to the nearest hundredth.

Math

Heights and Distances(a) An angle measures 37°. What is the measure of its supplement?
(b) An angle measures 26°. What is the measure of its complement?

Math

Heights and DistancesDistance Between Two Cargo Ships Ship A leaves port sailing north at a speed of 20 mph. A half hour later, Ship B leaves the same port sailing east at a speed of 35 mph. Let t (in hours) denote the time ship B has been at sea.
(a) Find an expression in terms of t giving the distance D between the two cargo ships.
D(t) =
(b) Use the expression obtained in part (a) to find the distance (in miles) between the two cargo ships 4 hr after Ship A has left port. (Round your answer two decimal places.)

Math

Heights and DistancesYou have an 11.5-meter giant friend who is standing at the top of a 1,010-meter mountain peak. What is the elevation at the top of your giant friend? Express in meters and kilometers, and in standard and scientific notation.