Jack’s eyes are 5 feet above the ground. He is standing 400 feet from the base of a building. His line of sight forms a 67° angl
e with the top of the building. How tall is the building?
2 answers:
Answer: 947.34 feet
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the trigonometric functions.
tan α = opposite side / adjacent side
Where α is the angle that His line of sight forms with the top of the building, the opposite side is the height of the building minus 5, and the adjacent side is the distance between him and the building (400)
Replacing with the values given:
tan 67 = x/ 400
Solving for x
tan 67 (400) =x
x= 942.34 feet
We have to add 5 feet, since we calculated the height of the building minus the eye level.
942.34 +5 = 947.34 feet
Feel free to ask for more if needed or if you did not understand something.
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Answer:
Let x be the width of the compartment,
Then according to the question,
The length of the compartment = x + 2
And the depth of the compartment = x -1
Thus, the volume of the compartment,
But, the volume of the compartment must be 8 cubic meters.
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⇒
⇒
If and if
But, width can not be the complex number.
Therefore, width of the compartment = 2 meter.
Length of the compartment = 2 + 2 = 4 meter.
And, Depth of the compartment = 2 - 1 = 1 meter.
Since, the function that shows the volume of the compartment is,
When we lot the graph of that function we found,
V(x) is maximum for infinite.
But width can not infinite,
Therefore, the maximum value of V(x) will be 8.
