math help please?

Question

Does extending the sides of an angle affect its size?
Yes
No
Both
Neither


30: Can there be a right triangle with sides 3", 4", and 9"?
Yes
No
Both
Neither


31: How high is a tree that casts a shadow 65 ft. long at the same time of day that a yardstick casts a shadow 45 inches long?
47 ft.
49.5 ft.
52 ft.
55.75 ft.


32: Use the Rule of Pythagoras to find the length of a diagonal wire brace on a door that is 3' wide and 8' high.
8.23 ft.
8.54 ft.
8.98 ft.
9.22 ft

Answer 1

First question.
No.

30.) No.
the longest side in a right triangle is always the hypotenuse (the other two sides are legs) and, by the pythagorean theorem,
(leg)² + (leg)² = (hypotenuse)²
Here, the sides with lengths 3" and 4" are the legs and
(leg)² + (leg)² = (3)² + (4)² = 25 = (5)²
=> so 3, 4, 5 is a right triangle, but 3, 4, 9 is not.

31.) 52 feet
You have to similar triangles (both are right triangles).
The first one has legs T and 65 feet (the T stands for "tree").
The second one has legs 1 yard (36") and 45".
Because the triangles are similar, the ratio of the legs of the first triangle = the ratio of the legs of the second triangle:
T/65 = 36/45
T = (36/45)· 65
T = 52 feet

32.) 3 and 8 are the legs of a right triangle
=> the wire is the hyputenuse
=> wire² = (leg)² + (leg)²
=> wire² = (3)² + (8)²
=> wire² = 73
=> wire = √73
=> wire = 8.54 ft long

Hope this helps.

Answer 2

Does extending the sides of an angle affect its size?

No



30: Can there be a right triangle with sides 3", 4", and 9"?

3^2 + 4^2 = 9 + 16 = 25
9^2 = 81
25 not equal 81
s0
No

31: How high is a tree that casts a shadow 65 ft. long at the same time of day that a yardstick casts a shadow 45 inches long?

tan a = L / 65 = l / 3.75
L = 65 l / 3.75

where l is the height of the yardstick...if you have it pluck it in and get the tree height in ft
47 ft.
49.5 ft.
52 ft.
55.75 ft.


32: Use the Rule of Pythagoras to find the length of a diagonal wire brace on a door that is 3' wide and 8' high.
3^2 + 8^2 = 73 => diagonal = 8.54 ft


8.54 ft.

Answer 3

Does extending the sides of an angle affect its size? NO

30: Can there be a right triangle with sides 3", 4", and 9"? NO

31: How high is a tree that casts a shadow 65 ft. long at the same time of day that a yardstick casts a shadow 45 inches long?

height of tree/ (65x12) = 36/45
height of tree = (36/45) x 780 = 624 inches (52 feet)

32: Use the Rule of Pythagoras to find the length of a diagonal wire brace on a door that is 3' wide and 8' high.

length^2 = 3^2 + 8^2
length^2 = 9 + 64
length = 8.54'

Answer 4

No.

No. If two sides are 3 and 4, the third side is 5.
3^2 + 4^2 =
9 + 16 = 25
= 5^2

36/45 = x /65
4/5 = x/65
(65 * 4)/5 = x
13 * 4 = x
x = 52

3^2 + 8^2 =
9 + 64 =
75 = (5 * sqrt(3))^2
=5 * 1.73
= 8.66

Answer 5

1.No,

2.Leave aside the rt angled triangle,There can't be even any other type of triangle having sides 3,4,9.
Its a rule that for triangle with sides a,b,c,the sum of any 2 sides must be greater than the third side(all combinations)

here 3+4=7<9,hence tr. not possible.
using ur geometry box ,try constructing one,I bet u can't.

3.
65 * 12 inches shadow=?(x) (1 ft =12 inches)
if
45 inch shadow=1 yard

x=( (65*12) * 1) / 45 yards

4.Diagonal brace will be hypotenuse of triangle formed by
width, length,diagonal
d=sqroot(3sq+8sq)=sqroot(64+9)=sqrt(73)=approx 8.54

Answer 6

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Answer 7

Extending the sides does not change the size of an angle.

30. No

31. 52

32. 8.54

Answer 8

1) no
2)3)4) a^2 + b^2 = c^2 in a right triangle.

Answer 9

Holly's right. At least present some insight as to why you don't understand the questions. This place is not for other people to do your homework for you.

Answer 10

well u should use not only phythagorus, but u should go more deep, to the applications of diffrentials, and read some maximum valus, and some the related values to the time, good luck