Note Taking Guide:
Unit: Trig
Lesson 8: Characteristics of Trig Ratios/Word problems
Part 1: How do they relate?
Use your calculator to evaluate.
1. sin 65°
_________
2. cos 25°
_________
3. sin 18°
_________
4. cos 72° __________
What do you notice?
5. Tan 25° _________
6. Tan (90-25)° _________
Part 2: More relationships!
4
3
& sin A 
5
5
cos C  __________ , sin C  __________ , and tan C  __________ .
1. ABC has the following characteristics: B  90 , cos A 
Draw it!
Note Taking Guide:
Unit: Trig
Lesson 8: Characteristics of Trig Ratios/Word problems
Practice:
1. If tan 
2. If sin 
5
, then tan 90     __________ .
13
6
, then cos  90     __________ .
10
Your Turn:
Part 3: Mixed up word problems!
1. Lenny is planning to cut down a pine tree and he wants to make sure that the
tree will not hit his truck when it falls. The tree casts a shadow that is 150 feet
long, and the angle of elevation from the base of the shadow to the top of the
tree is 50°.
a. How tall is the tree?
b. If Lenny parked his truck 90 feet away from the base of the tree, should he
move his truck?
2. A skateboard ramp is 6 feet long, and it stands 3 feet high. What is the angle of
elevation of the ramp to the ground?
3. We have a basic triangular shaped tent. The base of our tent is 10 feet wide and
the middle support pole is 6 feet high. At what angle does the tent touch the
ground?
6
---------10---------
Note Taking Guide:
Unit: Trig
4.
Lesson 8: Characteristics of Trig Ratios/Word problems
The “sin” button on your calculator is not working. Explain in words another way
to find the missing side. Find the missing side without using sine.
12
46°
5.
A
Find the perimeter of trapezoid ABCD
2
y
B
8
54º
D
6.
The angle of depression from the top of a flag pole to a point on the ground is
35°. If the point on the ground is 82 feet from the
35°
base of the flag pole, how tall is the pole?
82 feet
7.
A 5.5 foot person standing 10 feet from a street light casts a 14 foot shadow.
What is the height of the streetlight?
5.5
x˚
10
14
shadow
C
Note Taking Guide:
Unit: Trig
Lesson 8: Characteristics of Trig Ratios/Word problems
A
8.
Find the length of side AC given:
DB  15 in
B
D
ADB  17
ADC  37
C
9. The longer leg of a 30°-60°-90° triangle is 15 meters long. Find the perimeter.
10. If a diagonal of the square is 10 cm, what is the length of each side?
11. Find the altitude of an equilateral triangle, if each side of the triangle has a
length of 18 meters.