CC Geometry H
Aim #21: How do we solve problems involving special right triangles?
Do Now:
0
0
0
1. The shorter leg of a 30 -60 -90 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
45
P
300
0
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.
0
6. Each side of a rhombus is 14 in. long. Two of the sides form a 60 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
0
of sight to the top of the tower and the horizontal is 45 . He then walks a
certain distance east, and is then 100 ft from the base of the tower. The angle
0
between his line of sight to the top of the tower and the horizontal becomes 60 .
a) Determine the exact height of the tower,
and its height to the nearest tenth of a foot.
A
B
b) Determine the exact distance from the tourist's eye level to the top of the
tower from the second location.
0
0
0
8a) ΔXYZ is a 45 -45 -90 triangle
with right angle Z. Find the
coordinates of X in Quadrant IV
for Y(-1,2) and Z(6,2).
0
0
0
b) ΔEFG is a 30 -60 -90 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
side: 18 mm, perimeter: 72 mm
0
10. The diagonals of a rectangle are 12 in. long and intersect at an angle of 60 .
Find the perimeter of the rectangle.
6√3
6
600
300
6
6
600
600
12 + 12√3 units
6
6
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
0
line makes a 60 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
AD = 50 ft
FD = 25√3 ≈ 43.3 ft
E
F
20 ft
G
38.4 ft
D
12. A regular hexagon is made up of six equilateral triangles. Find AC in simplest
B 5 A 5
radical form.
AC = 10√3 10
5√3
300
C
Name ______________________
Date _________________
1. Find x and y.
y
a.
CC Geometry H
HW #21
b.
600
x0
9
12
y
x
3. Find x.
2. Find x, y and z.
450
y
450
600
18
450
z
450
450
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
D
7
13
50
B
0
0
0
6a) ΔJKL is a 45 -45 -90 triangle with
right angle K. Find the coordinates of
L in Quadrant IV for J(-3,5) and K(-3,-2).
C
0
0
0
b) ΔPCD is a 30 -60 -90 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 30
B
and AE =
, then what is the area of square ABCD?
A.
B. 16
A
C. 64
30
D. 72
C
E.
0
0
E
D
0
8. Imani needs to determine the height of a tree. Holding a drafter's 45
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