Special Right Triangles
45-45-90 and 30-60-90
1) Word problems to put things into context
a) A baseball diamond is a square with sides of 90 feet long.
i) To the nearest foot, what is the length of a throw from home to 2nd base?
ii) What is the length of a throw from the shortstop position to 1st base if the short stop is
midway between 2nd and 3rd base?
2) Exploring 45-45-90
a) Questions
i) What is an isosceles triangle?
ii) How would you describe an isosceles triangle?
iii) What is the angle measure of the two congruent angles in an isosceles right triangle?
How do you know?
iv) Can you form a conjecture about an isosceles right triangle and its angle
measurements?
Example of an isosceles triangle
B
m ABC = 45°
m ACB = 45°
m BAC = 90°
Segments AB and B C are called legs
Segment B C is called the hypotenuse
A
C
v) What is the Pythagorean Theorem?
vi) Can you find the length of ‘c’ using the Pythagorean Theorem for isosceles triangles?
1
5
8
c
8
5
c
c
1
c=?c=?c=?
vii) Form a conjecture between the length of the hypotenuse and the legs of an isosceles
triangle?
b) Given triangle ABC with a right angle at C: AC = BC = x, prove AB = x 2
A
x
x
C
B
c) How would you find the length of the legs of an isosceles triangle given the hypotenuse?
d) Solve the given problem.
Chuck
Alan
Brooke
Chuck, Alan, and Brooke are playing catch with each other.
To make things easy, they are stading in a triangle.
Chuck just had shoulder surgery, and is worried about hurting
his arm again. Chuck can throw the ball ten feet or less, and
his arm will be alright. If Brooke is throwing the ball 4 feet to Alan,
and Alan is throwing the ball 4 feet to Chuck, is Chuck able to safely throw
the ball to Brooke?
3) Exploring 30-60-90 right triangles
a) If triangle ABC is equilateral with altitude BD, what are the measures of:
ÐA, ÐB, ÐC, ÐABD, ÐDBC, ÐBDC
B
A
D
C
b) Solve for x and y in the following examples with 30-60-90 right triangle
B
B
8
8
y
A
x
8
C
D
AC = 8
10
y
A
x
D
24
y
60
y
60
x
x
c) Form a conjecture about 30-60-90 triangles regarding their angles and side lengths?
A baseball diamond is a square with sides of 90 feet long.
a) To the nearest foot, what is the length of a throw from home to 2nd base?
b) What is the length of a throw from the shortstop position to 1st base if the short stop is
midway between 2nd and 3rd base?