A boy 14m tall,stood 10m away from a tree of hight 12m calculate correct to the nearest degree, the angle of elevation of the top of the tree from the boys eyes hint:construct or draw the triangle with respect to the given sides
The angle of elevation of the top of the tree from the boy's eyes is approximately 53°.
Well, it seems like the boy has quite the view to tackle! Let's use a bit of imagination to draw out this situation.
We have a tree standing tall at 12 meters, a boy who's a modest 14 meters tall, and the distance between them is 10 meters.
Now, we can create a right triangle where the boy's height acts as one side, the distance between them acts as the base, and the height of the tree acts as the hypotenuse.
Applying some trigonometry, we can use the tangent function to find the angle of elevation. The tangent of an angle is equal to the opposite side (boy's height) divided by the adjacent side (distance between them).
So, let's calculate the angle:
tan(x) = opposite/adjacent
tan(x) = 14/10
Using a calculator, we find that x is approximately 53.1 degrees.
Therefore, the angle of elevation of the top of the tree from the boy's eyes is approximately 53.1 degrees.
Hope this helps! Now, didn't that mathematical circus make you feel taller too?
To solve this problem, we can use trigonometry and draw a diagram to visualize it.
Step 1: Draw a triangle where the boy's eyes are at the base, the tree's height is the vertical side, and the distance between the boy and the tree is the hypotenuse.
Boy's eyes
/|
/ |
/ |
/_____|
x (height of the tree)
Therefore, we have a right-angled triangle.
Step 2: Use the tangent function to find the angle of elevation. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
x (height of the tree)
___________
10m + * | (hypotenuse)
__________
Boy's eyes
The opposite side is the height of the tree (x), and the adjacent side is the distance between the boy and the tree (10m). So, we can write the equation:
tan(angle) = x / 10m
Step 3: Substitute the given values into the equation and solve for the angle.
tan(angle) = 12m / 10m
tan(angle) = 1.2
Step 4: Use the inverse tangent (arctan) function to find the angle.
angle = arctan(1.2) ≈ 50.19 degrees
Therefore, the angle of elevation of the top of the tree from the boy's eyes is approximately 50.19 degrees when rounded to the nearest degree.
To calculate the angle of elevation of the top of the tree from the boy's eyes, we need to use the concept of trigonometry and consider the triangle formed by the boy, the tree, and the vertical line connecting the boy's eyes to the top of the tree.
Let's call the angle of elevation θ (theta).
By drawing the triangle, we can see that the height of the tree (12m) is opposite to the angle θ, the distance from the boy to the tree (10m) is the adjacent side, and the boy's height (14m) is the hypotenuse.
Now, we can use the tangent function to solve for θ:
tan(θ) = opposite/adjacent
tan(θ) = 12/10
To find θ, we need to take the inverse tangent (arctan or tan^(-1)) of both sides of the equation:
θ = arctan(12/10)
θ ≈ 50.19 degrees (rounded to nearest degree)
So, the angle of elevation of the top of the tree from the boy's eyes is approximately 50 degrees.