What is the slant height x of the square pyramid?
Express your answer in radical form.

Answer:
x = [tex] 4 \sqrt { 3 } [/tex]
Step-by-step explanation:
We are given a diagram of a pyramid with a right angled triangle which has [tex]30[/tex]°, [tex]60[/tex]° and [tex]90[/tex]° angles an the hypotenuse is [tex]8cm[/tex].
Since we have a right angled triangle, we can apply sin here:
We know that [tex]sin 60 = \frac{\sqrt{3} }{2}[/tex] so we can write it as
[tex]\frac{\sqrt{3} }{2} = \frac{x}{8}[/tex]
So we get the slant height of x = [tex]4\sqrt{3}[/tex].
Answer:
The slant height of square pyramid = 4√3 m
Step-by-step explanation:
From the figure we can see a square pyramid with lateral edge 8 m
Also the one angle of face triangle is 60° , therefore the face triangle is an equilateral triangle.
Therefore the base is 8 m
To find the slant height
slant height² = Lateral edge² - (base/2)²
= 8² - (8/2)² = 8² - 4²
= 64 - 16 = 48
Slant height = √48 = 4√3 m
Therefore slant height of square pyramid = 4√3 m