- If a painter's 24-ft ladder is leaned
against a vertical wall to where the top of the ladder rests
against it at a height of 21½ ft,
find the measure of the angle formed between the ladder and the
level ground.
- The roof of a house is designated as a "5 and 12"
pitch, i.e., the ratio of the "rise to the
run" (see the illustration below). What is the measure
of the roof's angle of inclination (θ), rounded to the nearest
tenth of a degree?
- Grade is defined as the ratio of
the change in elevation (or vertical distance) to
the change in horizontal distance.
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- If a stretch of road has an 8% grade, then at what angle
measure is the road rising with respect to the horizontal?
Round the answer to the nearest half degree.
- If a car travels along this road for ¾-mi
what would be the car's change in elevation over this
distance? Express the answer rounded to the nearest whole
number of feet.
- A helicopter pilot reports to an air traffic controller that
he is currently hovering at an altitude of 750 m
and is at a (horizontal-ground) distance of 4 km
from the airport. At approximately what angle (of elevation)
measure, to the nearest whole degree, should the
controller aim his binoculars at a height of 20 m
(from the level ground) to spot the aircraft?
- If you hold a quarter at a distance of 2.5 feet
from your eye, find the measure of the angle formed between the
top and bottom of the coin with your eye as the vertex.
Exercise 5: You will need to measure the
diameter of a quarter.
- A 5'10" man is standing 100 yards
away from you. What angle measure represents the angle formed
between the top of the person's head, your eye (as the vertex),
and the bottom of the man's feet?
- The sun's radius is approximately 432,300 mi
and its distance from the Earth averages about 93 × 106
mi. Determine, to the nearest hundredth of a
degree, the measure of the angle formed between
the top and bottom of the sun's disc with your eye being the
vertex.
- The moon's diameter is approximately 2160 mi
and its distance from the Earth averages about 238,600 mi.
Determine, to the nearest hundredth of a degree,
the measure of the angle formed between the top and bottom of
the moon's disc with your eye being the vertex.
- NASA's space shuttles frequently orbit the Earth at an
altitude of about 200 mi.
What would be the maximum distance between two points on the
Earth's surface which can be seen simultaneously by astronauts
aboard a shuttle?
- Approximately 700 mi
above the Earth, a telecommunications satellite circumnavigates
the Earth. What is the maximum range between two points on the
Earth which can receive signals from the satellite at any given
time?
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