Answer:
1.96 m or 2m when rounded to nearest tenth
Step-by-step explanation:
The question is referring to a square right pyramid. The base is square and the perpendicular axis is vertical to the base.
These are the different parts of a square right pyramid .
See figure for detailed description(taken from Wolfram website)
The ones of interest here are
- a = base side length = = 2.1m (given).
It is same on all 4 sides = 1.5m (given)
- e = edge length = 1.5m (given)
This corresponds to each of the poles of the tent.
- Looking at the figure we can see the slant height
[tex]s^2 = r^2 + h^2[/tex] or [tex]\displaystyle s = \sqrt{r^2 + h^2[/tex]
This is the computation through the Pythagorean theorem where s forms the hypotenuse and r and h the two sides of a right triangle
- r is nothing but half the side length = 1.5/2 = 0.75m
- h has to be computed first. Looking at the figure we can see that half the diagonal of the base, the edge and the height all form a right triangle. Therefore
[tex]e^2 = (\dfrac{d}{2})^2 + h^2[/tex] - The diagonal of the square base is given by the formula
[tex]d = \sqrt{a^2 + a^2 }= \sqrt{2}a[/tex]
So d here = √2 a ;
d/2 = √2(a/2) = a/√2 - Substituting values for e=2.1, d = a/√2
==> 2.1² = (a/√2)² + h²
==> 2.1² = a²/2 + h²
==> (1.5²/2) + h² - After moving h² to the left side and the constants to the right we get
h² = 2.1² - 2.25/2 = 3.285 (do not find square root yet, we have to square again)
- Thus we get from substituting in formula for s²,
s² = r² + h²
s² = 0.75² + 3.285 = 0.5625 + 3.285 = 3.8475
s = √3.8475 = 1.96 m
Answer slant height s = 1.96 = 2 m when rounded to nearest tent
