Answer:
Step-by-step explanation:
Area of parallelogram = base * height
= 12 * 8
= 96 cm²
Area of parallelogram = 96
base * height = 96
base = 96/height
base = 96/16
base = 6 cm
Let ABC be a triangle in the 3rd quadrant, right-angled at B.
So, AB-> Perpendicular BC -> Base AC -> Hypotenuse.
Given: sinθ=-3/5 cosecθ=-5/3
According to Pythagorean theorem, square of the hypotenuse is equal to the sum of square of the other two sides.
Therefore in triangle ABC, 〖AC〗^2=〖AB〗^2+〖BC〗^2 ------
--(1)
Since sinθ=Perpendicular/Hypotenuse ,
AC=5 and AB=3
Substituting these values in equation (1)
〖BC〗^2=〖AC〗^2-〖AB〗^2
〖BC〗^2=5^2-3^2
〖BC〗^2=25-9
〖BC〗^2=16
BC=4 units
Since the triangle is in the 3rd quadrant, all trigonometric ratios, except tan
and cot are negative.
So,cosθ=Base/Hypotenuse Cosθ=-4/5
secθ=Hypotnuse/Base secθ=-5/4
tanθ=Perpendicular/Base tanθ=3/4
cotθ=Base/Perpendicular cotθ=4/3
A = 864
w = 2/3l
A = lw
Plug in what we know:
864 = l(2/3l)
Multiply:
864 = 2/3l^2
Divide 2/3 to both sides or multiply by its reciprocal, 3/2:
864 * 3/2 = l^2
2592/2 = l^2
1296 = l^2
Find the square root of both sides:
l = 36
So the length of the basement is 36 feet.
