Answer:
12cm and 16cm
Step-by-step explanation:
The hypotenuse of the right angle triangle = 20cm
let the other two sides be x and y;
The difference;
x = y - 4
Problem:
Find x and y;
Solution:
According to the pythagoras theorem;
x² + y² = 20² ------ i
x² + y² = 400 ----- i
and x - y = 4 ---- ii
So; x = 4 + y
Now input the value into equation (i);
(y + 4)² + y² = 400
(y+4)(y+4) + y² = 400
y² + y² + 4y + 4y + 16 = 400
2y² + 8y + 16 = 400
2y² + 8y + 16 -400 = 0
2y² + 8y - 384 = 0;
y² + 4y - 192 = 0
Factorize the equation;
y² + 16y - 12y - 192 = 0
y(y + 16) - 12(y + 16) = 0
(y-12)(y + 16) = 0
y -12 = 0 or y+ 16 = 0
y = 12 or -16
It is not realistic for the length of a body to be a negative value, so y= 12;
since;
x - y = 4,
x = 4 + 12
x = 16
13.) 15
14.) 13
15.) 8
16.) 5
17.) 12
18.)16
If the answers are in the standard form of a line then it would be -x + (-3x) = -5y. This is because the standard form of a line is written as Ax + Bx = Cy
For this case, the area is given by:
A = x * (200-2x)
Rewriting:
A = 200x-2x ^ 2
Deriving the expression we have:
A '= 200-4x
Equaling zero we have:
200-4x = 0
We clear x:
4x = 200
x = 200/4
x = 50 feet
Then, the maximum area is:
A (50) = 50 * (200-2 * 50)
A (50) = 5000 feet ^ 2
Answer:
the maximum possible area that can be enclosed with his 200ft of fencing is:
A (50) = 5000 feet ^ 2
4. What you want to do is first find the tan ratio, because tangent is opposite / adjacent, which you can use to find x.
So tan(52) = 1.28 ish. So we know that x/18 = 1.28.
Then multiply both sides by 18.
x / 18 * 18 = 1.28 * 18
x = about 23.
5. Now, you can use the pythagorean's theorem, a^2 + b^2 = c^2.
Just input all values.
18 ^ 2 + 23 ^ 2 = c ^ 2
324 + 529 = c ^ 2
853 = c^2
square root of 853 = c
x = 29.2 ish
6. In this case, use cosine, or adjacent / hypotenuse.
cos(16) = 0.96 ish
so that means 24/x = 0.96
Then basically,
24 / 0.96 = x
x = 25
So x = 25
Then you can use the Pythagorean's Theorem again. I'm not going to go as in depth.
a ^ 2 + b ^ 2 = c ^ 2
24 ^ 2 + b ^ 2 = 25 ^ 2
576 + b ^ 2 = 625
b ^ 2 = 49
b = 7
8. Use tan here. opposite/adjacent Again, not going as in depth.
tan(55) = 1.43 ish
1.43 = Y / 22
1.42 * 22 = Y
Y = 31.24 ish
Length of MN:
31.24 ^ 2 + 22 ^ 2 = c ^ 2
976ish + 484 = c ^ 2
1460 = c ^ 2
x = 38.2 ish
10. Use cosine.
cos(63) = about 0.45
Adjacent / hypotenuse
3 / x = 0.45
3 / 0.45= x
x = 6.67
And then pythagorean's Theorem.
6.67 ^ 2 = 3 ^ 2 + b ^ 2
44.5 = 9 + b ^ 2
35.5 = b^2
b = about 6
