Answer:the height of the balloon is 670.244 feet
Step-by-step explanation:
The right angle triangle BLD represents the scenario.
h represents the height of the balloon.
We would apply trigonometric ratio to determine h.
Tan # = opposite side/adjacent side
Looking at triangle LCD,
# = 61 degrees
h = opposite side
x = adjacent side
Tan 61 = h/x
1.7321 = h/x
h = 1.7321x
Looking at triangle LBD,
# = 54 degrees
h = opposite side
x + 100 = adjacent side
Tan 54 = h/x + 100
1.3764 = h/x + 100
h = 1.3764(x + 100)
Therefore,
1.7321x = 1.3764(x + 100)
1.7321x = 1.3764x + 137.64
137.64 = 1.7321x - 1.3764x
137.64 = 0.3557x
x = 137.64/0.3557 = 386.955
h = 1.7321x = 386.955 × 1.7321
h = 670.244 feet
Answer:
5/6
Step-by-step explanation:
5/10 can be simplified as 1/2
1/2 + 1/3 = 3/6 + 2/6 = 5/6
I am assuming that the whole 3x - 6 in the fraction is the numerator
the this simplifies to 3x (3x - 6)
= 9x^2 - 18x (C)
The volume inside is 27 cu. ft.
The surface area of a cube is the area of each face of the cube added together. There are 6 faces on a cube; 54/6 = 9 sq. ft. for each face of the cube.
Each face of a cube is a square, whose area is given by A=s²:
9 = s²
Take the square root of both sides:
√9 = √s²
3 = s
Each side of the square, or edge of the cube, is 3 ft.
This makes the volume 3(3)(3) = 27 cu. ft.