Download Chapter 7: Right Triangles and Trigonometry

Chapter 7: Right Triangles and Trigonometry
7.0 Simplify Radicals
Simplify each radical expression.
1) √12
4) �
60
3
2) 5√40
3) −3√108
5) −5√15 • −2√3
6)
√18
√24
•
√48
√12
7.1 Apply the Pythagorean Theorem
Example 1:
Identify the unknown side as a leg or hypotenuse. Then find the unknown side length of the right triangle.
Write your answer in simplest radical form.
1.
2.
3.
34
x
Example 2:
A 16 foot ladders rests against the side of a house, and the base of the ladder is 4 feet away. Approximately
how high above the ground is the top of the ladder.
Example 3:
Find the area of each triangle.
A)
B)
Example 4:
In your town, there is a field that is in the shape of a right triangle with the dimensions shown.
A) Find the perimeter of the field.
B) You are going to plant dogwood seedlings about every 10 feet around the edge.
How many trees do you need?
C) If each dogwood seedling sells for $12, how much will the trees cost?
Pythagorean triples
Example 5:
Given the 2 lengths of a right triangle, use a Pythagorean Triple to find the third length.
a) 24, 32
b) 24, 45
c) 40, 85
7.2 Pythagorean Theorem Converse
Example 1:
Tell whether the given triangle is a right triangle.
1)
2)
Example 2:
Tell whether the segments with the given side lengths can form a triangle. If so, classify the triangle as acute,
right, or obtuse.
a) 10.5, 36, 37.5
b) 8, 21, 27
c) 18, 23, 25.2
d) 30, 40, 60
7.4 Special Right Triangles
45–45–90
Example 1:
Find the lengths of each unknown sides (leave in simple radical form).
1.
2.
n
m
n
m
6
3.
4.
m
10
m
n
n
30–60–90
Example 2:
Find the lengths of the unknown sides. (Leave in simple radical form)
1.
y
2.
15
x
3.
4.
y
8
y
x
Example 3:
Find the lengths of the unknown sides. Leave your answer in simplest radical form.
1)
2)
a
600
c
b
18
d
7.5/7.6 Trigonometric Functions
• Trigonometric Ratio: _______________________________________________________________________
• Tangent: ________________________________________________________________________________
• Sine/Cosine: _____________________________________________________________________________
________________________________________________________________________________________
Sine, Cosine, and Tangent Ratios
SOH CAH TOA
Example 1:
Find the value of each variable. Round to the nearest hundredth if necessary.
1)
2)
3)
4)
Example 2:
Find the perimeter of each triangle. Round to the nearest tenth.
1)
2)
7.7 Solve Right Triangles
• To solve a right triangle, you need to __________________________________________________________
• You can solve a right triangle if you know:
– _________ side lengths
or
– _________ side length and the measure of _________ acute angle
How to Find Angle Degrees
Example 1:
Find the measure of each angle. Round to the nearest tenth.
1)
2)
3)
Example 2:
Solve the right triangle. Round decimals to the nearest hundredth.
1)
2)
3)