2. • The learner will identify
the angle of depression.
• The learner will solve
word problems involving
angle of depression.
• Recognize the
importance of angle of
depression in real life
situation.
Objectives:
3. Evaluate each trigonometric function
using calculator. Round of to the
nearest hundred thousandths.
•Sin 38º
•Tan 45º
•Tan 12º
•Cos 67º
•Cos 12º
4. The angle of depression is
formed when the observer is
higher than the object he/she is
looking at. When an observer
looks at an object that is situated
at a distance lower than the
observer, an angle is formed
below the horizontal line drawn
with the level of the eye of the
observer and line joining object
with the observer’s eye.
What is Angle of
Depression?
5. Example 1:
•From the top of the vertical cliff
that overlooks the ocean, a person
measures the angle of depression of
a boat at the sea as 9º. The height
of the cliff is 142 m. How far is the
boat from the base of the cliff?
6. Example 2:
•An airplane is flying at a height of 4
kilometers above the ground. The
distance along the ground from the
airplane to the airport is 6
kilometers. What is the angle of
depression from the airplane to the
airport?
7. • Sine
• Cosine
• Tangent
• Cosecant
• Secant
• Cotangent
What are the 6
trigonometric ratios?
8. • Sine
• Cosine
• Tangent
What are the 3
trigonometric ratios
that we can use in
our calculator?
9. The angle of depression is
formed when the observer is
higher than the object he/she is
looking at. When an observer
looks at an object that is situated
at a distance lower than the
observer, an angle is formed
below the horizontal line drawn
with the level of the eye of the
observer and line joining object
with the observer’s eye.
What is Angle of
Depression?
10. Example 3:
•A building stands on the bank of a
river. A man observes from a corner of
the roof of the building, the foot of a
electric post just on the opposite
bank. If the angle of depression of the
foot of the light post at your eye is 30°
and the height of the building is 12
meters, what is the width of the river?
11. Example 4:
•An observer on a cliff 1000 dm above
sea level sights two ships due east.
The angles of depression of the ships
are 47° and 32°. Find the distance
between the two ships to the nearest
decimeter.
12. Evaluation.
Solve the following problems involving
angle of depression.
1. From the top of a fire tower, a forest
ranger sees his partner on the
ground at an angle of depression of
40º. If the tower is 45 feet in height,
how far is the partner from the base
of the tower, to the nearest tenth of
a foot?
13. 2. A submarine starts on the surface,
and dives at an angle of 13º to the
surface. It goes diagonally a distance
of 890 meters before reaching the
bottom. How deep is the water where
the submarine reaches the bottom?
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