7.4 Special Right Triangles
Find the value of the variables of each isosceles triangle.
Write the answer in simplest radical form.
2.
1.
y
b
4
3
a
x
4.
3.
x
y
17√2
12√2
Thm 7.8
45º– 45º– 90º Triangle Theorem
In a 45º– 45º– 90º triangle, the hypotenuse is
long as each leg.
times as
45º
Hyp = leg ∙_____
x
45º
x
Ex 1: Find the length of the hypotenuse.
a.
b.
8
3√2
3√2
45º
x
x
Ex 2: Find the length of the legs of the triangle.
15√2
x
x
Guided Practice: Find the value of the variable.
8
2.
1.
2√2
x
8
x
d
8
3. Find the leg length of a 45º – 45º – 90º triangle with a
hypotenuse length of 6.
Pages 461 – 464 # 1–7, 11, 29, 30, 33, 36
8
Ex 1 Find the value of x.
5
45º
x
Ex 2 Find the value of x.
x
12
4
Thm 7.9 30º– 60º– 90º Triangle Theorem
In a 30º– 60º– 90º triangle, the hypotenuse is 2 times as long
as the shorter leg and the longer leg is
√3 times as
long as the shorter leg.
Hypotenuse = 2 ∙ shorter leg
= 2 ∙ SL
Hyp
30º
2x
x√3
Longer leg = shorter leg ∙ √3
= SL ∙ √3
LL
60º
x
Ex 1: Find the values of x and y. Write your answer in
simplest radical form.
60º
y
x
30º
9
Ex 2: Find the values of a and b. Write your answer in
simplest radical form.
b
60º
a
30º
15
Pages 461 – 464 # 8–10, 12, 16–25, 27, 28, 31, 32
Ex 3 Find the value of f and g.
f
60º
10
g
Ex 4 Find the values of a and b.
30º
7
a
b