Download Problems Involving Right Triangles

Masterful Mathematics
Problems Involving
Right Triangles
1. A ladder is 8.0 m long is placed against a window of a building as shown.
How high will the ladder reach up against the wall of the building ?
2. How far is the foot (bottom) of the ladder away from the building?
3. A boat is stationed off shore in the ocean. The boat looks toward the shore and notices a vertical cliff as
shown in the picture. How far is the boat from the shore?
4. What is the distance to the cliff looking along the “sight line”? (hint: hypotenuse)
5. If an airplane sits on the runway of an airport under the cover of a fog bank, as shown below. Use your
knowledge of Trigonometric Functions to determine the height of the fog bank above the runway in
meters if the distance b = 2.00 km and  = 27.4 ° as shown below.
Right Triangle Trig Problems
1
revised: 8/24/2012
6.
What is the altitude of an equilateral triangle with a side of 4 inches?
7.
If a square is 7ft on a side, what is the length of the diagonal?
8.
A six-foot tall person walks from the base of a streetlight directly toward the tip of a shadow cast by the streetlight.
When the person is 16 feet from the streetlight and 5 feet from the tip of the streetlight’s shadow, the person’s shadow
starts to appear beyond the streetlight’s shadow.
A) Draw the right triangle that is the visual representation of the problem. Label the sketch with the known
quantities, then label the unknown items with a variable. Be sure to indicate the height of the streetlight
with a variable.
B) Use trigonometric functions to write an equation for the unknown quantity. Then find the height of the
streetlight.
9.
Height: A 30-meter line is used to tether a helium balloon. Due to a breeze, the tethered line makes a 75° with the
ground.
A) Draw a right triangle that is the visual representation of the problem. Label the sketch with the known
quantities, then label the unknown items with a variable. Be sure to indicate the height of the streetlight
with a variable.
B) Use trigonometric functions to write an equation for the unknown quantity. Then find the height of the
balloon.
10. Width: A biologist wants to know the width of a river in order to properly set the instruments to study the pollutants
in the water. From point A, the biologist walks downstream 100 feet (to a point B) and sights point C
(which is a point directly across the river from point A) . How wide is the river ?
B
w
58°
A
C
11. CHALLENGE PROBLEMS:
An Architect wants to design a house that provides some
passive solar energy features. To do this, he designs the house
to control the sun exposure on the south facing wall. From a
standard sun reference book, the architect determines that at the
latitude of the house (40°N latitude) that the sun has an angle of
75° during the summer months, and a 27° during the winter
months (both measurements are taken at noon). If the house is
19ft tall, then how much overhang should she provide so that
the shadow of the noonday sun will reach the bottom of the
wall ?
12. How far down the wall will the shadow of the overhang reach
at noon during the winter?
Right Triangle Trig Problems
2
revised: 8/24/2012