Respuesta :
Answer: h= 69.3m
Step-by-step explanation:
The correct values in the question are:
year : 2006, length 62, vertical height 62.
So, the measure asked is called slant height . we have to apply the formula:
sh = √(vh^2 + [L/2]^2)
Where:
vh= vertical height
L= length of a side of the square base
Replacing with the values given:
sh= √(62^2 + [62/2]^2)
sh = √(3,844 + 31^2)
sh= √(3,844 + 961)
sh = √4,805
hs= 69.31 =69.3 m (nearest tenth)
Since in the question that height is called h, h= 69.3
The height h of each of the triangular faces of the pyramid with height 62 meter and square base of 62 m side length is 69.3 m approx.
What is Pythagoras Theorem?
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
For this case, the pyramid has base as square with sides 62 m
The vertical height of the pyramid is 62 m too.
Assuming the pyramid is symmetric, we have all those 4 triangular faces of the pyramid symmetric too.
Considered the diagram above.
We drop a perpendicular from the top of the pyramid to center of the base (it falls on the center because of symmetry).
Now, we get a triangle ABC which is a right angled triangle.
The length BC is half of the length of the sides of the base of the pyramid parallel to it because of it being center of a square and parallel to its two sides (provable mathematically).
Now, we get:
- BC = half of the side length of base of pyramid = 62/2 = 31 m
- AB = vertical height of pyramid = 62 m
- AC = height of one of the triangular faces (and therefore, height of each of those 4 triangular faces because of all being congruent due to symmetry).
Using the Pythagoras theorem, we get:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\|AC|^2 = 62^2 + 31^2 = 4805\\\\\\\text{Taking positive root of both the sides}\\\\|AC| = \sqrt{4805} \approx 69.3 \: \rm m[/tex]
(positive only because |AC| is length which is a non-negative quantity).
Thus, the height h of each of the triangular faces of the considered pyramid is 69.3 m approx.
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
