mathematics?

Question

If a triangle has sides of lengths 8, 10 and 13, is the triangle right?
Yes
No
Sometimes
Not enough information


10: If a triangle has sides of lengths 8, 4, and 4 sqrt(3), is the triangle right?
Yes
No
Sometimes
Not enough information


11: Refer to right triangle ACB. If m Ang A = 30° and BC = 5, what is the length of AC?
5 sqrt(2)
5
5 sqrt(3)
10


12: Refer to right triangle ACB. If m Ang A = 30° and BC = 5, what is the length of AB?
5 sqrt(2)
5
5 sqrt(3)
10


13: Refer to right triangle ACB. If m Ang A = 30° and AC = 9 sqrt(3), what is the length of BC?
3 sqrt(3)
3
9
18


14: Refer to right triangle ACB. If m Ang A = 30° and AC = 9 sqrt(3), what is the length of AB?
3 sqrt(3)
3
9
18


15: Refer to right triangle ACB. If m Ang A = 45° and BC = 3, what is the length of AC?
3 sqrt(3)
3
3 sqrt(2)
1.5
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Answer 1

I am reproducing the questions and am giving the answers below each.

If a triangle has sides of lengths 8, 10 and 13, is the triangle right?
Yes
No
Sometimes
Not enough information

8 X 8 + 10 X 10 = 164 and 13 is not square root of 164. So, No is the answer.


10: If a triangle has sides of lengths 8, 4, and 4 sqrt(3), is the triangle right?
Yes
No
Sometimes
Not enough information

4 x 4 + 4sqrt3 x 4 sqrt3 = 16 + 48 = 64 = 8 x 8

Yes, it is a right angled triangle. 8 is the hypotenuse.


11: Refer to right triangle ACB. If m Ang A = 30° and BC = 5, what is the length of AC?
5 sqrt(2)
5
5 sqrt(3)
10

BC/AC = tan 30 and AC = BC/tan 30 = 5sqrt3 ( tan 30 = sin30/cos30 = 1/sqrt3)


12: Refer to right triangle ACB. If m Ang A = 30° and BC = 5, what is the length of AB?
5 sqrt(2)
5
5 sqrt(3)
10

BC/AB = sin 30 or AB = BC/sin 30 = 5/0.5 = 10


13: Refer to right triangle ACB. If m Ang A = 30° and AC = 9 sqrt(3), what is the length of BC?
3 sqrt(3)
3
9
18

BC/AC = tan 30 or BC = AC tan 30 = 9sqrt3 x 1/sqrt3 = 9


14: Refer to right triangle ACB. If m Ang A = 30° and AC = 9 sqrt(3), what is the length of AB?
3 sqrt(3)
3
9
18

AC/AB = cos 30 or AB = AC / cos 30 = 9sqrt3/ sqrt3 / 2= 9 /sqrt3 X 2/sqrt3 = 18


15: Refer to right triangle ACB. If m Ang A = 45° and BC = 3, what is the length of AC?
3 sqrt(3)
3
3 sqrt(2)
1.5

Since ACB is a right angled triangle, if A is 45, BC and AC must be equal. So, AC will also be equal to 3.
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Answer 2

9 -10, use the pythagorean theorem to solve.

9) a^2+b^2=c^2
8^2+10^2=13^2
164 is not equal to 169, therefore the triangle is NOT right.

10) 4^2+(4sqrt3)^2=8^2
64=64, therefore the triangle is right

11-15 use SOH CAH TOA to solve

11) tan30=5/x
tan30x=5
tan30x/tan30=5/tan30
x=8.660, or 5sqrt3

12) sin30=5/x
sin30x=5
sin30x/sin30=5/sin30
x=10

13) tan30=x/(9sqrt3)
(9sqrt3)tan30=x
x=9

14)cos30=(9sqrt3)/x
cos30x=9sqrt3
cos30x/cos30=(9sqrt3)/cos30
x=18

15)tan45=3/x
tan45x=3
tan45x/tan45=3/tan45
x=3

I hope this helps! :)

Answer 3

you should do this by yourself but one the first on you use the formula: a^2+b^2=c^2(and the second)

1. a=8
b=10
c=13

a^2+b^2=c^2
8^6+10^2=13^2
just solve

Answer 4

Dude, I'll tell you what: I'll do your homework for you if we can trade ages. What a combination: My brain in a young body like yours!