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Geometry UNIT : Triangles
Topic: Right Triangle Trigonometry
Lesson: Tic-Tac-Toe Trigonometry
Content Objective
To use trigonometric ratios in problem
Language Objective
G.11(C ) develop, apply, and justify triangle similarity
relationships, such as right triangle ratios, trigonometric
ratios, and Pythagorean triples using a variety of methods
Sine, cosine, tangent ratios
Prior Knowledge
Students need to know how to set up trigonometric ratios in order to solve for a missing
Set of problems copied on cardstock
Tic-Tac-Toe Board
Recording Sheet
Teacher Notes:
Each pair or group of students will get a set of the word problems. Some problems are
more complex than others. Students should draw a picture of each problem they are
solving, label it, and then solve and answer the question. Some of the questions require
the students to explain in the form of a written response.
You may decide to have the students complete on tic-tac-toe in class, and another tic-tactoe for further practice.
Ramp It Up
In order for ramps to be accessible for individuals with
disabilities, there are requirements placed on the design
of the ramps. One requirement is that the slope of the
ramp cannot rise more than 1 inch for each foot.
Therefore, the slope of the ramp cannot be greater than
Brooke is designing a ramp to install at her business. In her design, the ramp makes a
5° angle with the ground and is 24 feet long. Will her ramp meet the requirements for
individuals with disabilities outlined above? Justify your answer with a drawing and
written explanation.
Airplane Landing
Commercial airliners fly at an altitude of about 10 kilometers.
They start descending toward the airport when they are far away,
so that they will not have to dive at a steep angle.
If the pilot wants the plane’s path to make an angle of 3 degrees with the ground, what is
the distance the plane will travel on this descending path?
Submarine Problem
A submarine at the surface of the ocean makes an emergency dive, its path
making an angle of 21 degrees with the surface.
If it goes for 300 meters along its downward path, how deep will it be?
How tall is it?
A boy, who is 5’6’’ tall, stands on a sidewalk, looks up at a tall house, and
wonders how tall it is. Using a meter stick and a clinometers (instrument used
to measure the angle of elevation or depression), he determines the
measurements shown.
About how tall is the building?
The Ascending Airplane
The climb angle (angle of elevation) of an airplane
taking off is 20º. If the airplane maintains that angle
until it reaches cruising altitude, what is the
approximate horizontal ground distance from that
airplane to the point of takeoff when the airplane has
reached its cruising altitude of 30,000 feet?
(Remember that 1 mile = 5,280 feet.)
The Lookout Tower
Park rangers use lookout towers to watch
for forest fires at great distances. A ranger
at the top of a 200-foot tower spots a fire and
measures the angle of depression as 2º. How
far away is the fire?
The Ferris Wheel
A Ferris wheel at a local park has
eight chairs, and the radius of the
wheel is 12 feet. It is shown in the
nearby diagram. What is the
approximate height of the blue
chair above the platform?
The Lighthouse
A lighthouse that is 50 meters above sea level marks the entrance to a bay. The
lighthouse is used to orient ships as well as to provide a lookout point for the local
coast guard.
A pair of ocean kayakers estimate their distance to the entrance of the bay using the
lighthouse. They measure the angle of elevation from their position to the top of the
lighthouse to be about 16°. Draw a diagram showing the kayaks in relation to the
lighthouse illustrating the angle of elevation.
Knowing the height of the lighthouse and the angle of elevation from the kayakers to
the top of the lighthouse, calculate the kayakers’ distance to the entrance of the bay.
Statue of Liberty
Linda gets a nose-bleed whenever she is 300 feet above ground.
During a class fieldtrip, her teacher asked if she wanted to
climb to the top of the Statue of Liberty. Since she does not
want to get a nose-bleed, she decided to take some
measurements to figure out how high the
torch of the statue is .
She found a spot directly under the torch and then measured 42 feet away and
determined that the angle up to the torch was 82°. Her eyes are 5 feet above
the ground.
Should she climb to the top or will she get a nose-bleed? Draw a diagram that
fits this situation. Justify your conclusion.
Tic-Tac-Toe Trigonometry
The Ferris Wheel
The Lighthouse
The Descending
Airplane Landing
Statue of Liberty
The Look Out Tower
The Ascending Airplane
The Tall House
Ramp it Up
Tic-Tac-Toe Recording Sheet
Write the name of the problem. Draw a picture
and label it.
Solve the problem.