Geometry Chapter 7 - Right Triangles and Trigonometry Section 7.4 - Special right triangles
What the student should get from this: !" Justify and apply properties of a 45˚-45˚-90˚ right triangle #" Justify and apply properties of a 30˚-60˚-90˚ right triangle Let’s start again with the Pythagorean Theorem... The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. B c a
C
b
A
But now we’ll change the triangle to an isosceles right triangle. (The 45˚-45˚-90˚ right triangle) That means that
.
c a
a In a 45˚-45˚-90˚ triangle !"#$"%&'!#()*#$+*$,,,,,,,,,,,,,$-.#*$/*$0'(1$/*$/$0#12 Example 1: given the following isosceles right triangles, solve for x.
x
6 in.
6 in.
x
x
in.
The other special right triangle is the 30˚-60˚-90˚ right triangle. This is where it comes from: That means that
x
.
x h
x !"#$%#&'()*+ 3($/$30˚-60˚-90˚$!4+/(10#5$!"#$"%&'!#()*#$+*$,,,,,,,,,,,,,$$/*$0'(1$/*$!"#$*"'4!#4$0#15$/(6$!"#$ 0'(1#4$0#1$+*$,,,,,,,,,,$-.#*$/*$0'(1$/*$!"#$*"'4!#4$0#12
Example 2: given the following 30˚-60˚-90˚ triangles, solve for x and y. 10 ft x
10 ft
10 ft
x
x
y
y y
Example 3: Solve for x, y and z. 45˚
x 12 ft
y
y
x
45˚
30˚
z
60˚
x
y
Example 4: Find the perimeter and area of each figure. A 45˚-45˚-90˚ triangle with hypotenuse of 14.5 inches.
A 30˚-60˚-90˚ triangle with long leg of 6 inches.
Example 5: Find the coordinates of point P where is a 45˚-45˚-90˚ triangle with vertices Q(4, 6) and R(-6, -4), and . P is in quadrant II.
Show work to get credit Assignment: p.461 #s 8-18 all, 23-26, all, 34. Due next class. One class period late will be 50% off. Beyond that, no credit given.