Honors Geometry WORKSHEET
Applications of Trigonometric Ratios
NAME____________________________
PERIOD________DATE______________
DIRECTIONS: Draw a picture (if not already given), label appropriate sides and/or angles in the
triangle, and use what you know about right triangles (Pythagorean Theorem,
SOHCAHTOA ratios, sum of angles in a triangle = 180˚, etc.) to solve:
1.) A salvage ship is locating underwater
wreckage. The ship’s sonar picks up
a signal showing wreckage at an angle
of depression measuring 12˚. The
ocean charts for this region show a
level ocean floor with an average
depth of 40 meters. If a diver is
lowered from the salvage ship at
this point, how far can the diver
expect to travel along the ocean floor
to the wreckage?
2.) According to a Chinese legend from the Han dynasty (206 BCE – 220 CE), General Han Xin flew a
kite over the palace of his enemy to determine the distance between his troops and the enemy
palace. If the general let out 800 meters of string and the kite was flying at a 35˚ angle of
elevation, approximately how far away was the palace from General Han Xin’s position?
3.) Benjamin is flying a kite directly over his buddy Franklin, who is 125 meters away.
His kite string makes a 39˚ angle with the ground. To the nearest meter,
how high is the kite?
4.) The angle of elevation from a boat
to the top of a 42-meter lighthouse
on the shore measures 33˚. To the
nearest meter, how far is the boat
from the shore?
42 m
33˚
5.) Meteorologist Wendt Storm is using a sextant to determine the height of a weather balloon.
When she views the weather balloon through her sextant, which sits 1 meter above the level
ground, she measures a 44˚ angle up from the horizontal. The radio signal from the balloon
tells her that the balloon is 1400 m from her measuring device.
(a) To the nearest meter, how high is the balloon?
(b) To the nearest meter, how far is it to a position
directly below the balloon?
Continued on the back
6.) A lighthouse is observed by a ship’s officer at a 42˚ angle to the path of the ship. At the next
sighting, the lighthouse is observed at a 90˚angle to the path of the ship. The distance traveled
between sightings is 1800 m. To the nearest meter, what is the distance between the ship and
the lighthouse at this second sighting?
Trigonometry applied to Geometry:
DIRECTIONS: Use your calculator to approximate each indicated length or angle. Express each
answer accurate to the nearest hundredth.
7.)
>>
8.)
17 m
h
20 m

32˚
>>
 = ____________________
h = ____________________
9.)
18 m
10.)
12 cm
r
h
32˚
58˚
40 cm
r = ____________________
11.)
56˚
20”
h = ____________________
12.)
d
>>
a
2.7 m
14”
62˚
d = ____________________
13.)
>>
a = ____________________
14.)
8’
16 cm
d
10’

28 cm
15’
 = ____________________
d = ____________________