As we can see the given diagram represents an isosceles trapezoid.
So we can say from the properties of isosceles trapezoid.
As the required side XY has a length y+1, So we can write
Sec^2 x - 1 = tan^2x
Proof:
Sec^2x = 1+ tan^2x
1/cos^2x = 1 + sin^2x/cos^2x
<span>1/cos^2x - sin^2x/cos^2x = 1
</span>Using common denominator:
(1-sin^2x)/cos^2x = 1
sin^2x + cos^2 x = 1
cos^2 x = 1 - sin^2x
Substituting :
cos^2x/<span>cos^2x = 1
</span>1 = 1
Left hand side = right hand side
Answer:
x = -1, y = 2 and z = -4.
Step-by-step explanation:
-2x + 5y + 4z = -4 ......(A)
-5x - y + z = -1 .............(B)
2y + 2z = -4..................(C) Multiply (A) by 5 and (B) by -2:
-10x + 25y + 20z = -20 ....(D)
10x + 2y - 2z = 2 ..............(E) Adding D + E:
27y + 18z = -18 Dividing by 9:
3y + 2z = -2 ............(F) Subtract: (C) - (F):
-y = -2
y = 2.
Substitute for y is (C):
4 + 2z = -4
2z = -8
z = -4.
Substitute for y and z in (A):
-2x + 5(2) + 4(-4) = -4
-2x = -10 + 16 - 4 = 2
x = -1.
You can set this up as 2 fractions equal to each other, like ratios.
18/11=108/x
Cross multiply and you get 18x=1,188
Now divide both sides by 18 and get x.
x=66.
If the height of the building is 108ft, the width is 66ft.
