Transcript 8.7 Applications of Right Triangle Trigonometry

8.7 APPLICATIONS OF RIGHT
TRIANGLE TRIGONOMETRY
Some critical terminology
 Horizontal  any line constructed so that it is parallel with
the horizon or another horizontal line.
 Line of Sight  the line from the observer’s eye to the object
 Angle of Elevation  if the object being observed is above
the horizontal then the angle between the line of sight and
the horizontal is called the Angle of Elevation.
 Angle of Depression  if the object being observed is below
the horizontal then the angle between the line of sight and
the horizontal is called the Angle of Depression.
 Angle of Inclination  if the line of sight follows a physical
object, such as an inclined plane or a hillside, we use the
term Angle of Inclination.
Diagram of terminology.
Angle of Depression
Horizontal
Horizontal
Angle of Elevation
The hardest part of these story problems is drawing the
picture and deciding what you are being asked to find.
An observer on the 1st floor of an airport control
tower sights an airplane at an angle of elevation of
32◦. The pilot reports the plane’s altitude is 3.5 km.
What is the plane’s horizontal ground distance from
the tower?
A helicopter pilot sights a life raft. The angle of
depression is 26° and the helicopter’s altitude is
3km. What is the plane’s distance from the raft?
A monument casts a shadow 215 ft long
when the angle of elevation of the sun is
52°. Find the height of the monument.
The length of a guywire supporting a radio tower
is 175 ft. The angle of elevation created by the
guywire and ground is 65°. How tall is the tower?
The tailgate of a moving van is 3.5 feet
above the ground. A loading ramp is
attached to the rear of the van at an incline
of 10°. Find the length of the ramp.
Oscar is in a lighthouse on a cliff. He
observes 2 sailboats due east of the
lighthouse. The angles of depression to the
2 boats are 33° and 57 °. Find the distance
between the 2 sailboats if the top of the
lighthouse measures 803 feet from sea level.
A pilot is flying at 10,000 feet and wants to
take the plane up to an altitude of 20,000 feet
over the next 50 miles. What should his angle
of elevation be to accomplish this task?
Two observers are 200 feet apart, in line with a
tree containing a bird’s nest. The angles of
elevation to the bird’s nest are 30 ° and 60 °. How
far is each observer from the base of the tree? Is
there difference 200?
Driving along a straight flat stretch of Arizona highway, you
spot a particularly tall saguaro ("suh-WARH-oh") cactus
right next to a mile marker. Watching your odometer, you
pull over exactly two-tenths of a mile down the road.
Retrieving your son's theodolite from the trunk, you
measure the angle of elevation from your position to the
top of the saguaro as 2.4°. Accurate to the nearest whole
number, how tall is the cactus?
You were flying a kite on a bluff, but you managed somehow to
dump your kite into the lake below. You know that you've given
out 325 feet of string. A surveyor tells you that the angle of
declination from your position to the kite is 15°. How high is
the bluff where you and the surveyor are standing?
A lighthouse stands on a hill 100 m above sea level. If ∠ACD
measures 60° and ∠BCD is 30°, find the height of the
lighthouse.
John wants to measure the height of a tree. He walks exactly 100 feet from
the base of the tree and looks up. The angle from the ground to the top of
the tree is 33º . How tall is the tree?
An airplane is flying at a height of 2 miles above the ground. The distance
along the ground from the airplane to the airport is 5 miles. What is the
angle of depression from the airplane to the airport?
To measure the width of a crater on Mars, the Mar’s Probe
travels at an altitude of 5.3 km above Mar’s surface. The
onboard guidance system measured the angles of
depression to the far and near edges of the crater and
found them to be 14° and 23° respectively. Find the distance
across the crater.