Please I need help ASAP
1 answer:
You might be interested in
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.
The height of the tower is 331.3 meters
The distance from the car to the foot of the tower is 191.3 meters
The situation forms a right angle triangle.
<h3>Right angle triangle:</h3>Right angle triangle has one of its angles as 90 degrees. Therefore,
The height of the tower is the opposite side of the right angle triangle. The distance from the foot of the tower to the car is the adjacent side of the triangle formed.
Therefore, the following trigonometric can be formed from the relationship.
let
x = adjacent side = distance from the foot of the tower to the car.
Therefore,
cross multiply,
(140 + h)(tan 45) = h tan 60
140 tan 45 + h tan 45 = h tan 60
140 tan 45 = h tan 60 - h tan 45
140 = h√3 - h
140 = 1.732h - h
140 = 0.732h
h = 140 / 0.732
h = 191.256830601
h = 191.3
Therefore,
height of the tower = 140 + 191.3 = 331.3
The distance from the car to the foot of the tower is as follows;
- x = 191.3 / tan 45
x = 191.3 / 1
x = 191.3
Therefore, the distance from the car to the foot of the tower is 191.3 meters
learn more on right triangle here; brainly.com/question/26750565?referrer=searchResults