A tree, in danger of falling , stands 65 feet from the house. The angle of elevation from the bottom of the house to the top of the tree is 50 degrees. If the tree should fall directly towards the house, will it the house?
show all work and explain your answer.
tan50/1=x/65
x=65tan50
x=77
the tree would hit the house if it falls because it is 77ft tall, and the house is only 65 ft away.
Is this correct?
thanks for checking my work
yes, 65 tan 50 is 77.5 so crash
By the way, we know any angle greater than 45 degrees will cause a crash without doing any arithmetic. At 45 degrees the tree is 65 feet high.
Thank you for your help, That is interesting to see it like that, but if we don't show all the work we don't get credit for the question
Yes, your calculation is correct. Let's go through the steps.
First, we can set up a right triangle with the bottom of the house, the top of the tree, and the distance between them (65 feet). The angle of elevation is given as 50 degrees.
To determine if the tree will hit the house, we need to find the height of the tree and compare it to the distance between the tree and the house.
Using the tangent ratio, we can set up the equation:
tan(50 degrees) = opposite/adjacent
tan(50 degrees) = x/65
To solve for x (which represents the height of the tree), we can rearrange the equation:
x = 65 * tan(50 degrees)
Plugging in the values and calculating:
x ≈ 77
So, the height of the tree is approximately 77 feet.
Since the height of the tree is greater than the distance between the tree and the house (65 feet), the tree would hit the house if it falls directly towards it.
Therefore, your answer is correct.