- The largest living organism in the world today is a tree
in Sequoia National Park named the "General Sherman." To
determine this tree's height, park rangers marked off a
distance of 185 ft
from (the center of) its base and then measured the angle of
elevation to the top of the tree to be 56°04'.
Approximately how tall was the General Sherman if measured
in:
- An office building casts a shadow of 50 m
when the sun's angle of elevation is found to be 60.4°.
Determine the approximate height h of the office
building when it is measured in:
a. meters
b. feet
A painter leans his 24 ft
ladder against a wall where the angle made with the level
ground is 70°. For each of the following, round the answer
to the nearest whole number of feet and
inches
- How far up the wall does the top of the ladder
reach?
- How far is the bottom of the ladder from the wall?
- A 200 meter
high antenna needs to be secured to the ground with a series
of guy wires. The angle formed with the (level) ground is
designated to be 60°. How long does each guy wire need to
be? Round the answer to the nearest foot.
A ground radar indicates that a Federal Express
cargo plane is approaching from a line-of-sight
distance of 2.5 miles.
If the plane's angle of elevation is 15°40', at
what altitude is the airplane flying? Round the
answer to the nearest hundred feet.
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- A television
tower stands on the top of the One Shell Plaza building in
Houston, Texas. From a point 3000 ft
from the base of the building, the angle of elevation to the
top of the tv tower is θ = 18°26". If the
building is 714 ft
tall, how tall is the tower (to the nearest foot)?
- Find the Area for
each of the following triangles.
a.  |
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b.  |
- A forest ranger atop a 100 m
observation deck watches a wild fire progress toward his
position.
- He measures the angle of depression to the leading
edge of the fire to be 5°6'. How far is the fire from
the ranger's position?
- Two and one-quarter minutes later,
he measures the angle of depression again, finding it
has changed to 5°54'. How far is the fire from the
ranger's position at this time?
- What is the speed, in km/hr, at
which the fire is moving toward the ranger?
- If the fire continues to advance at the same speed,
then how many minutes after the second sighting before
the fire reaches the ranger's observation deck?
- An overzealous trigonometry student, stands near the
edge of a bridge overlooking a highway which passes
underneath 30 feet
below his line-of-sight. He times an oncoming car as it
passes a point in front of him where the angle of depression
is 10° until it is directly beneath his position on the
bridge. If the car travels the distance between these two
points in 2 sec, then
find whether or not the car is exceeding the posted 55 mph
speed limit.
- The distances between many astronomical bodies are so
extremely vast that scientists typically use units of
measure known as an Astronomical Unit (A.U.)
or a light-year (ly). In
addition to these two units, another unit is the
parsec (pc). One pc
is defined as the distance at which 1 A.U.
of arc length subtends an angle of 1". If an
A.U. is 150,000,000 km,
determine the number of light-years (rounded
to the nearest hundredth) in one parsec.
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