Question

the isosceles triangle in the diagram below represents the side view of a pyramid in egypt. which of these can be used to determine x, the slant height of the pyramid? 9 of 11 questions sin 46° = 375/x cos 46° = 375/x cos 46° = 750/x sin 46° = 750/x

Explanation:

Step1: Analyze the right - triangle formed

The base of the isosceles triangle is \(750\) ft. When we drop a perpendicular from the apex of the isosceles triangle (which is the height of the pyramid \(500\) ft), it bisects the base. So the adjacent side to the \(46^{\circ}\) angle in the right - triangle is \(\frac{750}{2}=375\) ft, and the hypotenuse is \(x\) (the slant height).

Step2: Recall the cosine formula

The cosine of an angle in a right - triangle is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 46^{\circ}\), the adjacent side \(a = 375\) ft, and the hypotenuse \(h=x\). So, \(\cos46^{\circ}=\frac{375}{x}\)

Answer:

\(\cos46^{\circ}=\frac{375}{x}\) (the second option)