Section 7.4 ~ Special Right Triangles
Topics in this lesson:
• 45­45­90 triangles
• 30­60­90 triangles
Objective: Use special right triangles to
find missing side lengths.
45o ­ 45o ­ 90o Triangle Theorem
In a 45­45­90 triangle, the hypotenuse is √2 times as long as each leg.
hypotenuse = leg x √2 There are 2 ways you can work with these:
Proportion method
Equation method
Plug in what you know. Solve for what you don't know.
x √2
=
hypotenuse
Every 45­45­90 triangle is similar to the one below, so put corresponding pieces in a proportion and solve for what you want.
leg
1
√2
45o
1
Example 1
Find the value of the variable.
a) b)
.
30o ­ 60o ­ 90o Triangle Theorem
In a 30­60­90 triangle, the hypotenuse is twice as long as the short leg, and the long leg is √3 times as long as the short leg.
hypotenuse = 2 x short leg
long leg = short leg x √3
You have the same two options here: equation method or proportion method.
Every 30­60­90 triangle is similar to this one: 1
2
√3
Example 2
Find the values of x and y. Write your answer in simplest radical form.
Example 3
Find the value of x.