The figure shows a person estimating the height of a tree by looking at the
1 answer:
Answer:
The proportion that can be used to estimate the height of the tree is option;
A.
Step-by-step explanation:
The given parameters in the question are;
The medium through which the person looks at the top of the tree = A mirror
The angle formed by the person and the tree with the ground = Right angles = 90°
The distance of the person from the mirror, d₁ = 5 ft.
The height of the person, h₁ = 6 ft.
The distance of the tree from the mirror, d₂ = 12 ft.
The angle formed by the incident light from the tree on the mirror, θ₁ = The angle of the reflected light from the mirror to the person, θ₂
Let 'A', 'B', 'M', 'T', and 'R' represent the location of the point at the top of the person's head, the location of the point at the person's feet, the location of the mirror, the location of the top of the tree and the location of the root collar of the tree, we have;
TR in ΔMRT = The height of the tree = h, and right triangles ΔABM and ΔMRT are similar
The corresponding legs are;
The height of the person and the height of the tree, which are AB = 6 ft. and TR = h, respectively
The distances of the person and the tree from the mirror, which are BM = 5 ft. and MR = 12 ft. respectively
∴ The angle formed by the incident light from the tree on the mirror, θ₁ = ∠TMR
The angle of the reflected light from the mirror to the person, θ₂ = ∠AMB
Given that θ₁ = θ₂, we have;
tan(θ₁) = tan(θ₂)
∴ tan(∠TMR) = tan(∠AMB)
From tan(∠TMR) = tan(∠AMB), we have;
The height of the tree, h = 14.4 ft.
Therefore, from the proportion the height of the tree can be estimated.
You might be interested in
For the first part:
Every shirt she grabs, will cost her dollars, so if she grabs 3 shirts, then the cost of the shirts is:
With the same rationale, if she grabs 2 pairs of jeans, the cost of the jeans is:
So, her total is:
If you subtract 3 from the total, then the expression is:
For the second part:
If she's paying 3 less for each shirt, then the cost of 3 shirts will become:
In the same fashion, for the two jeans:
So the expression for the total cost is:
For number three:
The amounts are different because the cost of the total purchase is different than the cost of each element that makes up the total purchase.
For number four:
If you're the owner, you want to give the smallest amount of discount (the one in part 1/a).
So you could clarify by saying there's 3 dollars of the TOTAL purchase's cost.
Every shirt she grabs, will cost her dollars, so if she grabs 3 shirts, then the cost of the shirts is:
With the same rationale, if she grabs 2 pairs of jeans, the cost of the jeans is:
So, her total is:
If you subtract 3 from the total, then the expression is:
For the second part:
If she's paying 3 less for each shirt, then the cost of 3 shirts will become:
In the same fashion, for the two jeans:
So the expression for the total cost is:
For number three:
The amounts are different because the cost of the total purchase is different than the cost of each element that makes up the total purchase.
For number four:
If you're the owner, you want to give the smallest amount of discount (the one in part 1/a).
So you could clarify by saying there's 3 dollars of the TOTAL purchase's cost.