Transcript Geometry 8.5

Geometry 8.5
STEPS to Solving Trig WORD PROBLEMS
1. Make a DRAWING
Geometry 8.5
STEPS to Solving Trig WORD PROBLEMS
1. Make a DRAWING
2. Label the known SIDES and ANGLES.
Geometry 8.5
STEPS to Solving Trig WORD PROBLEMS
1. Make a DRAWING
2. Label the known SIDES and ANGLES.
3. Determine whether you seek a:
Side – use SIN, COS, or TAN
Angle – use SIN-1, COS-1, of TAN-1
Geometry 8.5
STEPS to Solving Trig WORD PROBLEMS
1. Make a DRAWING
2. Label the known SIDES and ANGLES.
3. Determine whether you seek a:
Side – use SIN, COS, or TAN
Angle – use SIN-1, COS-1, of TAN-1
4. Write the Standard EQUATION and SUBSTITUTE.
Geometry 8.5
STEPS to Solving Trig WORD PROBLEMS
1. Make a DRAWING
2. Label the known SIDES and ANGLES.
3. Determine whether you seek a:
Side – use SIN, COS, or TAN
Angle – use SIN-1, COS-1, of TAN-1
4. Write the Standard EQUATION and SUBSTITUTE.
5. Use Algebra and Solve.
Geometry 8.5
STEPS to Solving Trig WORD PROBLEMS
1. Make a DRAWING
2. Label the known SIDES and ANGLES.
3. Determine whether you seek a:
Side – use SIN, COS, or TAN
Angle – use SIN-1, COS-1, of TAN-1
4. Write the Standard EQUATION and SUBSTITUTE.
5. Use Algebra and Solve.
6. Apply the SMELL Test to the Answer.
Geometry 8.5
IMPORTANT DEFINITIONS
Angle of ELEVATION –
The Angle an ASCENDING Line
Makes with the GROUND.
Angle of DEPRESSION –
The Angle a DESCENDING Line
Makes FROM a Line
PARALLEL with the GROUND.
Geometry 8.5
Geometry 8.5
Since the Angle of DEPRESSION and the Angle of
ELEVATION are on opposite, interior sides of a
TRANSVERSAL, they are ________________________.
Geometry 8.5
AIRPLANE Problem.
A plane is flying over level ground at an ALTITUDE
of 900 m.
The Pilot’s line of sight with the landing field makes
an Angle of Depression of 27.
Find the GROUND DISTANCE from the point directly
below the plane to the Landing Field.
MAKE A DRAWING
LABEL Sides and Angles
Geometry 8.5
AIRPLANE Problem.
A plane is flying over level ground at an ALTITUDE
of 900 m.
The Pilot’s line of sight with the landing field makes
an Angle of Depression of 27.
Find the GROUND DISTANCE from the point directly
below the plane to the Landing Field.
What Trig Equation?
Geometry 8.5
AIRPLANE Problem.
A plane is flying over level ground at an ALTITUDE
of 900 m.
The Pilot’s line of sight with the landing field makes
an Angle of Depression of 27.
Find the GROUND DISTANCE from the point directly
below the plane to the Landing Field.
Geometry 8.5
ANOTHER Plane Problem
A plane if flying over level ground at an ALTITUDE
of 7,000 ft.
When the pilot sights a landing field, the measure
of the angle of DEPRESSION is 32.
Find the GROUND DISTANCE to the Landing Field.
Geometry 8.5
A HEIGHT Problem
A tree 50 feet high casts a
35 foot shadow.
Find the measure of the
Angle of ELEVATION of
the
SUN.
Geometry 8.5
A HEIGHT Problem
A tree 50 feet high casts a
35 foot shadow.
Find the measure of the
Angle of ELEVATION of
the
SUN.
Geometry 8.5
ANOTHER HEIGHT Problem
A BUILDING 275 ft. tall casts a 160-ft shadow.
Find the measure of the Angle of Elevation
of the TOP of the Building.
Geometry 8.5
A LADDER Problem
A 20 ft. LADDER is leaning
against a wall.
The foot of the ladder forms
a angle measuring 65 with
the ground.
How are is the top of the
ladder from the GROUND?
Geometry 8.5
A LADDER Problem
A 20 ft. LADDER is leaning
against a wall.
The foot of the ladder forms
a angle measuring 65 with
the ground.
How are is the top of the
ladder from the GROUND?
Geometry 8.5
Another LADDER Problem
A 40-ft ladder is leaning against a building.
The ladder forms a 70 degree angle with the ground.
How far is the bottom of the ladder from the bottom
of the building?
Geometry 8.5
Amy is flying her kite in the park.
While she holds one end of the 60-foot kite string,
the kite floats at an angle of elevation of 40.
How HIGH is the kite above the ground?
Geometry 8.5
A cowboy must ride his horse across an open field
to a point 4 km to the South and 16 km to the East
of his present location.
What direction must the cowboy ride?
How FAR must the cowboy ride?
Geometry 8.5
The wire support for a telephone pole is 20 m. long.
If the angle of depression of the wire is 25 feet,
how TALL is the telephone pole?
Geometry 8.5
A storm cloud is traveling toward the center of a
large city.
It is currently 120 miles west and 35 miles south
of the city.
If it is to hit the city, what direction will the storm travel?
How far with the storm travel.?
Geometry 8.5
Geometry 8.5
Geometry 8.5
Geometry 8.5
Geometry 8.5
Geometry 8.5
Geometry 8.5
CIRCUS
ACTS
Geometry
8.5 At the circus, a person in the audience at
ground level watches the high-wire routine. A 5-foot-6-inch tall
acrobat is standing on a platform that is 25 feet off the ground.
How far is the audience member from the base of the platform,
if the angle of elevation from the audience member’s line of
sight to the top of the acrobat is 27°?
Answer:
The audience member is about 60 feet from the base of
the platform.
Geometry 8.5
DIVING At a diving competition, a 6-foot-tall diver stands
atop the 32-foot platform. The front edge of the platform
projects 5 feet beyond the ends of the pool. The pool itself is 50
feet in length. A camera is set up at the opposite end of the pool
even with the pool’s edge. If the camera is angled so that its
line of sight extends to the top of the diver’s head, what is the
camera’s angle of elevation to the nearest degree?
Answer:
40°
Vernon is on
the top deck of a cruise ship and observes two
Geometry
8.5
dolphins following each other directly away from the ship in
a straight line. Vernon’s position is 154 meters above sea
level, and the angles of depression to the two dolphins are
35° and 36°. Find the distance between the two dolphins to
the nearest meter.
Answer:
The distance between the dolphins is JK – KL. JL – KL
≈ 219.93 – 211.96, or about 8 meters.
Madison looks out her second-floor window, which is 15 feet
Geometry 8.5
above the ground. She observes two parked cars. One car is
parked along the curb directly in front of her window, and the
other car is parked directly across the street from the first car.
The angles of depression of Madison’s line of sight to the cars
are 17° and 31°. Find the distance between the two cars to the
nearest foot.
Answer: 24 ft
Geometry 8.5
Geometry 8.5
Geometry 8.5