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.

/Geo_Sec._7.4