Concept Category: The Relationship between the Unit Circle & Trigonometric Ratios
Learning Target :1AI can find a side or angle of a right triangle using sine, cosine, or tangent
Routine Problems
1.) Angle of Depression A person standing 150 centimeters from a mirror notices that the angle
of depression from his eyes to the bottom of the mirror is 12D , while the angle of elevation to the
top of the mirror is 11D . Find the vertical dimension of the mirror.
2.) Width of a Sand Pile A person standing on top of a 15-foot high sand pile wishes to
estimate the width of the pile. He visually locates two rocks on the ground below the base of
the sand pile. The rocks are on opposite sides of the sand pile, and he and the two rocks are in
the same vertical plane. If the angles of depression from the top of the sand pile to each of the
rocks are 27D and 19D , how far apart are the rocks?
3.)Height of a Door From a point on the floor the angle of elevation to the top of a door is 47D ,
while the angle of elevation to the ceiling above the door is 59D . If the ceiling is 10 feet above
the floor, what is the vertical dimension of the door?
Test yourself by creating
the diagram from the
problem with out looking
at the figure.
Concept Category: The Relationship between the Unit Circle & Trigonometric Ratios
Learning Target :1AI can find a side or angle of a right triangle using sine, cosine, or tangent
Topographic Map Reading Use the following diagram for problems 4-5:
The picture below shows a hiking trail and the location of three friends Stacey, Amy and Travis.
Keep in mind that S stands for Stacey’s position, A stands for Amy’s position and T stands for
Travis’ position :
4.) If the distance between Amy and Travis on the map is 0.5 inch, Find the angle of elevation
from Travis to Amy.
5.) If the distance between Stacy and Travis on the map is
5
inch, Find the angle of elevation
8
from Travis to Stacey.
6.) Height of a Tree Two people decide to find the height of a tree. They position themselves
25 feet apart in line with, and on the same side of, the tree. If they find that the angles of
elevation from the ground where they are standing to the top of the tree are 65D and 44D , how tall
is the tree?
Concept Category: The Relationship between the Unit Circle & Trigonometric Ratios
Learning Target :1AI can find a side or angle of a right triangle using sine, cosine, or tangent
7.) Height of a Tree An ecologist wishes to find the height of a redwood tree that is on the
other side of a creek as shown in the Figure. From point A he finds that the angle of elevation
to the top of the tree is 10.7D . He then walks 24.8 feet at a right angle from point A to point B.
There he finds that the angle between AB and a line extending from B to the tree is 86.6D . What
is the height of the tree?
8.) Height of a Tree To estimate the height of a tree, one person positions himself due south of
the tree, while another person stands due east of the tree. If the two people are the same
distance from the tree and 35 feet from each other, what is the height of the tree if the angle of
elevation from the ground at each person's position to the top of the tree is 48D ?
Concept Category: The Relationship between the Unit Circle & Trigonometric Ratios
Learning Target :1AI can find a side or angle of a right triangle using sine, cosine, or tangent
Routine Problems( Answers)
1.) 61cm
2.)
3.) 6.4 ft
Concept Category: The Relationship between the Unit Circle & Trigonometric Ratios
Learning Target :1AI can find a side or angle of a right triangle using sine, cosine, or tangent
4.)14.0
5.)
Concept Category: The Relationship between the Unit Circle & Trigonometric Ratios
Learning Target :1AI can find a side or angle of a right triangle using sine, cosine, or tangent
6.)
7.) 78.9
Concept Category: The Relationship between the Unit Circle & Trigonometric Ratios
Learning Target :1AI can find a side or angle of a right triangle using sine, cosine, or tangent
8.)