Aim #21: How do we solve problems involving special right triangles?
CC Geometry H
Do Now:
1. The shorter leg of a 300-600-900 triangle is 6 ft. Find the length of the other
two sides, to the nearest tenth of a foot.
2. The hypotenuse of an isosceles right triangle is 8.4 in. Find the length of each
leg to the nearest tenth of an inch.
Exercises: Special Right Triangles
1. Find x and y.
y
a.
6
b.
13
x
450
x0
c.
y
y
d.
300
x
x
y
600
2. Find x, y and z, and the perimeter of trapezoid PQRS.
S
10
R
x
300
450
P
y
z
Q
3. Find the exact length of the diagonal of a square 30 cm on a side.
4. The length of the altitude of an equilateral triangle is
a side of the triangle.
. Find the length of
5. The perimeter of an equilateral triangle is 39 cm. Find the length of an
altitude of the triangle.
6. Each side of a rhombus is 14 in. long. Two of the sides form a 600 angle. Find
the exact area of the rhombus, and its area to the nearest square inch.
7. A tourist's eye level, A, is 5'6" above level ground. The angle between his line
of sight to the top of the tower and the horizontal is 450. He then walks a
certain distance east, and is then 100 ft from the base of the tower. The angle
between his line of sight to the top of the tower and the horizontal becomes 600.
a) Determine the exact height of the tower,
and its height to the nearest tenth of a foot.
b) Determine the exact distance from the
tourist's eye level to the top of the tower from the
second location.
8a) ΔXYZ is a 450-450-900 triangle
with right angle Z. Find the
coordinates of X in Quadrant IV
for Y(-1,2) and Z(6,2).
A
B
b) ΔEFG is a 300-600-900 triangle
with m≮F = 90. Find the coordinates
of E in Quadrant III for F(-3,-4)
and G(-3,2). FG is the longer leg.
9. The length of the diagonal of a square is
square. mm. Find the perimeter of the
10. The diagonals of a rectangle are 12 in. long and intersect at an angle of 600.
Find the perimeter of the rectangle.
11. A zip line is anchored in one corner of a course shaped like a rectangular
prism. The other end is anchored in the opposite corner as shown. a) If the zip
line makes a 600 angle with post AF, find the zip line's length, AD.
b) Find FD, to the nearest tenth of a foot.
B
A
600
C
25 ft
E
F
20 ft
G
38.4 ft
D
12. A regular hexagon is made up of six equilateral triangles. Find AC in the
A
B
regular hexagon shown.
10
300
C
Name ______________________
Date _________________
1. Find x and y.
a.
12
b.
y
60
CC Geometry H
Hwk. #21
x0
0
9
y
x
3. Find x.
2. Find x, y and z.
450
y
450
600
18
450
z
450
45
0
x
6
x
4. The length of an altitude of an equilateral triangle is 12 feet. Find the length
of a side of the triangle.
5. Find the perimeter of quadrilateral ABCD.
27
A
13
50
B
6a) ΔJKL is a 450-450-900 triangle with
right angle K. Find the coordinates of
L in Quadrant IV for J(-3,5) and K(-3,-2).
D
7
C
b) ΔPCD is a 300-600-900 triangle
with right angle C and CD the longer
leg. Find the coordinates of P in
Quadrant III for C(1,-6) and
D
(1,7).
7. In the figure, square ABCD is attached to ΔADE as shown. If m≮EAD is 300
and AE =
A.
B. 16
C. 64
D. 72
E.
B
, then what is the area of square ABCD?
A
300
C
E
D
8. Imani needs to determine the height of a tree. Holding a drafter's 450
triangle so that one leg is horizontal, she sights the top of the tree along the
hypotenuse as shown. If she is 6 yards from the tree and her eyes are 5 feet
from the ground, find the height of the tree.
450
5 ft
6 yd
Mixed Review
1. Find x, y and z.
15
y
19
x
z
J
2. Given: JF bisects
EFG, EH ll FG, EF ll HG
Prove:
K
E
Statements
H
Reasons
F
G