The diagonal of the square creates two congruent right triangles, which you could see if you drew a picture. The diagonal is the hypotenuse of the triangle, and the sides of the square are the legs of the triangle. Again, a diagram might help.
The pythagorean theorem is (a^2)+(b^2)=(c^2), where c is the hypotenuse and a and b are the legs.
We know that c is 5 square root of 2, so:
(a^2)+(b^2)=((5 square root of 2)^2),
Now, distribute the square (exponent of 2) to both the 5 and the square root of 2. Squaring and the square root cancel each other out, leaving us with 2. 5^2 is 25. Then, both of those are multiplied together, so:
(a^2)+(b^2)=50
Since we are dealing with a square, both side lengths are the same, so a and b are the same number. So, we have two of the same term being added to each other. To eliminate any confusion, let x stand for the length of the sides of the triangle. This is equivalent to:
2(x^2)=50.
Then, we just solve for x.
(x^2)=25
x=5
All sides of the triangle are 5. So, the area is 5*5, or 25 inches.
Slope of AB = (5 - 2)/(7 - 4) = 3/3 = 1
slope of BC = (2 - 2)/(4 - 9) = 0
m<span>∠ABC = arctan 1 = 45°
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Answer:
x = 2√3 ≈ 3.464
Step-by-step explanation:
The side marked x is opposite the given 30° angle. The side marked 6 is adjacent to that angle. The trig function relating opposite and adjacent sides of a right triangle is ...
Tan = Opposite/Adjacent
Filling in values, we have ...
tan(30°) = x/6
Multiplying by 6 gives ...
x = 6tan(30°) = 6(√3/3)
x = 2√3 ≈ 3.464
Y varies with x
so y/ x = constant
so, y1/x1 = y2/x2
6/9 = 18 / x2
so x2 = ( 9*18)/6
x2 = 27
another solution
y varis with x
y inceased by 3 times
so x must increase 3 time of the intial value
x(new) = 9*3 = 27