Question

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

Answer 1

Answer:

x = $4 \sqrt { 3 }$

Step-by-step explanation:

We are given a diagram of a pyramid with a right angled triangle which has $30$°, $60$° and $90$° angles an the hypotenuse is $8cm$.

Since we have a right angled triangle, we can apply sin here:

We know that $sin 60 = \frac{\sqrt{3} }{2}$ so we can write it as

$\frac{\sqrt{3} }{2} = \frac{x}{8}$

So we get the slant height of x = $4\sqrt{3}$.

Answer 2

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