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Let the length of second side be x" ,
So,
Length of first side = 2" shorter than second = ( x - 2 )"
Length of third side = 5" longer than second = ( x + 5 )"
=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=
Given, perimeter = 33"
= > first side + second side + third side = 33"
= > ( x - 2 ) + x + ( x + 5 ) = 33
= > x - 2 + x + x + 5 = 33
= > 3x + 3 = 33
= > 3x = 30
= > x = 10
Hence, length of each side is
First side = ( x - 2 )" = ( 10 - 2 )" = 8 inches
Second side = x " = 10 inches
Third side = ( x + 5 )" = ( 10 + 5 )" = 15 inches
So,
Length of first side = 2" shorter than second = ( x - 2 )"
Length of third side = 5" longer than second = ( x + 5 )"
=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=
Given, perimeter = 33"
= > first side + second side + third side = 33"
= > ( x - 2 ) + x + ( x + 5 ) = 33
= > x - 2 + x + x + 5 = 33
= > 3x + 3 = 33
= > 3x = 30
= > x = 10
Hence, length of each side is
First side = ( x - 2 )" = ( 10 - 2 )" = 8 inches
Second side = x " = 10 inches
Third side = ( x + 5 )" = ( 10 + 5 )" = 15 inches
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
