*You will be able to find the lengths of sides of special right triangles 45-45-90 And 30-60-90.
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Transcript of *You will be able to find the lengths of sides of special right triangles 45-45-90 And 30-60-90.
*You will be able to find the lengths of sides of special right triangles
45-45-90
And
30-60-90
45-45-90 Right Triangle
a
aThis is our reference triangle for the 45-45-90.
2a
45
45
3
?
a
a
EX: 1 Find the Hypotenuse.
a 23 245
Reference Triangle
10?
EX: 2 Find the Hypotenuse.
5 2
5 2a
aa 2
Reference Triangle
x
6
EX: 3 Find the length of the leg.
3 2x
45
a
aa 2
Reference Triangle
Ex. 4 What is the length of the diagonal of this square?
17
1717 2
Standardized Test Practice
The correct answer is B.
30-60-90 Right Triangle
a
2a
60º
This is our reference triangle for the 30-60-90 triangle.
3a
30º
60
30
x8
Ex: 1 – Solve for x and y.
2a
60º
30º
a
3a
Reference Triangle
y
60
30
x
y
2a
60º
30º
a
3a
Reference Triangle
9
Ex: 2 – Solve for x and y.
60
30
x
y
5 3
Ex: 1 – Solve for x and y.
2a
60º
30º
a
3a
Reference Triangle
ANSWER 3 ANSWER 3 22 3
EXAMPLE 5 Find a height
Dump Truck
The body of a dump truck is raised to empty a load of sand. How high is the 14 foot body from the frame when it is tipped upward at the given angle?
EXAMPLE 5 Find a height
When the angle of elevation is 45, the body is about 9 feet 11 inches above the frame.
o
When the body is raised 45 above the frame, the height h is the length of a leg of a triangle. The length of the hypotenuse is 14 feet.
a.45 - 45 - 90
ooo
o
a. 45º angle
Solution
EXAMPLE 5 Find a height
When the angle of elevation is 60, the body is about 12 feet 1 inch above the frame.
o
b. When the body is raised 60, the height h is the length of the longer leg of a triangle. The length of the hypotenuse is 14 feet.
30 - 60 - 90ooo
o
b. 60º angle
Solution
Page 154 #23 & 24
Page 155 #1-13odd, 14-24
