 In
a right triangle, the square of the length
of the hypotenuse is equal to the sum of the
squares of the lengths of the legs

a2 + b 2 = c 2
a,
leg
c, hypotenuse
b, leg

a set of 3 positive integers a, b, and c that
satisfy the equation a2 + b2 = c2.
 3,4,5
5,12,13
8,15,17
7,24,25
and multiples of these numbers like….
 6,8,10
10,24,26 16,30,34 14,48,50
5
x
12
2 14
2 5
x
A
ramp for a truck is 6 feet long. The bed of
the truck is 3 feet above the ground. How
long is the base of the ramp?
20in.
20in.
24in
b
a
b
a
c
c
c
c
a
b
a
b
 If
the square of the length of the longest side
of a triangle is equal to the sum of the
squares of the lengths of the other two sides,
then the triangle is a right triangle.
 If c2 = a2 + b2, then triangle ABC is a right
triangle.
 If
c2 < a2 + b2 , then the triangle is acute.
 If
c2 > a2 + b2 , then the triangle is obtuse.
A
Given
Diagram:
c
b
a
C
P
b
R
x
a
Q
B
 Given
Diagram:
A
c
b
P
C
b
R
x
a
Q
a
B
 Theorem
- If the altitude is drawn to the
hypotenuse of a right triangle, then the two
triangles formed are similar to the original
triangle and to each other.
 If CD is an altitude of
ABC, then
C
CBD ~
ABC ~
ACD
A
D
B
 Identify
the similar triangles
D
G
E
F
 Side
view of a tool shed
 What is the maximum height of the shed to
the nearest tenth?
8ft
15ft
9ft
17ft
 In
a right triangle, the altitude from the right
angle to the hypotenuse divides the
hypotenuse into two segments. The length of
the altitude is the geometric mean of the
length of the two segments
C
A
D
B
 In
a right triangle, the altitude from the right
angle to the hypotenuse divides the
hypotenuse into two segments. The length
of each leg of the right triangle is the
geometric mean of the lengths of the
hypotenuse and the segment of the
hypotenuse that is adjacent to the leg.
C
A
D
B
 Find
K
2
k
10
 45o-45o-90o
Triangle TheoremIn a 45o-45o-90o triangle, the hypotenuse
is √2 times as long as each leg.
 In
a 30o-60o-90o triangle, the hypotenuse is
twice as long as the shorter leg and the
longer leg is √3 times as long as the shorter
leg.
A
logo in the shape of an equilateral triangle
 Find the height of the logo.
 Each side is 2.5 inches long.
 Trigonometric
Ratio- a ratio of the lengths of
two sides of a right triangle.
SOH – CAH- TOA

B
a
C
c
b
A
 Tangent-
ratio of the length of the opposite
leg to the adjacent leg of a right triangle
(Round to 4 decimal places.)- “TOA”
D
45
E
75
60
F
 Find
x. Round to the nearest tenth.
9
17
X
 Find
the height of the flagpole to the nearest
foot.
65 
24ft
 Sine
“SOH”
 Cosine
“CAH”
B
a
C
c
b
A
 Solve
the right triangle formed by the water
slide.
X
42 
50ft
Z
Y
 Inverse

sin
sin-1
If sin A = y, then sin-1 y= m<A
 Inverse

tan-1
If tan A = x then, tan-1 x = m<A
 Inverse

tan
cos
cos-1
If cos A = z, then cos-1 z = m<A
B
a
C
c
b
A
 Angle
C is an acute angle in a right triangle.
Approximate the m<C is to the nearest tenth
degree when:

Sin C = 0.2400

Cos C = 0.3700
 Approximate
the measure of angle Q to the
nearest tenth of a degree.
R
12
Q
8
S
A
road rises 10 feet over a 200 foot
horizontal distance. Find the angle of
elevation.
 To
solve a right triangle means to find the
measures of all of the sides and angles.
 You


need:
2 side lengths or
one side and one angle
 Angle
of Elevation- the angle your line of
sight makes with a horizontal line while
looking up
 Angle of Depression- the angle your line of
sight makes with a horizontal line while
looking down
angle of depression
angle of elevation
 You
are skiing down a mountain with an
altitude of 1200m. The angle of depression
is 21o. How far do you ski down the
mountain? Round to the nearest meter.
 You
are looking up at an airplane with an
altitude of 10,000ft. Your angle of elevation
is 29o. How far is the plane from where you
are standing? Round to the nearest foot.
15
120
20
P(x,y)
r
