Name:
Period:
Trigonometry
APPLICATIONS
36) Points A and B are on opposite sides of the Grand
Canyon. Point C is 200 yards from Point A. Angle B
measures 87° and Angle C measures 67°. What is the
distance between Point A and Point B?
35) Mark, Ivan, and Juan are camping in their tents. If the
distance between Mark and Ivan is 153 feet, the distance
between Mark and Juan is 201 feet, and the distance
between Ivan and Juan is 175 feet, what is the angle
between Ivan, Juan, and Mark?
34) Claire climbed to the top of a 164 foot lighthouse and
spotted a water fountain on the ground below. If the
angle of depression from the lighthouse to the fountain
is 54°, how far is the fountain from the base of the
lighthouse?
33) Jack is at the zoo looking up at a monkey sitting on top
of a pole. His eyes are 5 feet above the ground. If Jack is
standing 24 feet from the base of the pole and the angle
of elevation from Jack to the top of the pole is 23°, find
the height of the pole.
SIN
COS
TAN
=
=
=
(CAH)
(TOA)
(SOH)
Give the trig ratio as a fraction for each angle.
1) Sin A =
3) Cos A =
5) Tan A =
2) Sin B =
4) Cos B =
6) Tan B =
!
29) Find BC
30) Find mÐC
31) Find mÐB
32) Find AB
Law of Cosines
___________________ represents a relationship between ___________ and __________ of a triangle.
It works for angle measures between _____ and ______.
!!"#"$$$$$$$$$$$$$$$$$$$"
%!"#"$$$$$$$$$$$$$$$$$$$"
&!"#"$$$$$$$$$$$$$$$$$$$"
Solving for a side
Solving for an angle
28) Find BC
29) Find mÐA
Solve for x.
7)
8)
9)
10)
Trigonometric Ratios
!"#!"#$𝜃 %&
'()!"#$𝜃 %&
23) Find AB
24) Find BC
25) Find mÐC
26) Find mÐC
Law of Sines
*+#!"#$𝜃 %&
For any ΔABC, the ratio _________________ to the length of_________________ is constant.
This means that:
=
=
This property is called _________________. It works for angles between ______ and ______.
Solving for a side
Solving for an angle
21) Find BC
22) Find mÐA
Find the missing angle.
11)
12)
13)
14)
Inverse Trigonometry
45°- 45°- 90°
30°- 60°- 90°
The sides of this
triangle are always in
the ratio
The sides of this
triangle are always in
the ratio
__________
__________
Solve for the missing sides:
Solve for the missing sides:
Solve for the missing sides.
15)
16)
17)
18)
19)
20)
Special Right Triangles