Find the angle,in degrees,between two adjacent sides of the pyramid shown below.Round to the nearest tenth of a degree.[Note: The base of the pyramid is not considered a side.] P(8,0,0),Q(8,8,0),R(0,8,0),S(4,4,4)
A)54.7°
B)30°
C)2.1°
D)90°
E)45°

Question

Find the angle,in degrees,between two adjacent sides of the pyramid shown below.Round to the nearest tenth of a degree.[Note: The base of the pyramid is not considered a side.]  P(8,0,0),Q(8,8,0),R(0,8,0),S(4,4,4)
A)54.7° 
B)30° 
C)2.1° 
D)90° 
E)45°

Quizplus · Accepted Answer

First, we need to find the length of the slant height of the pyramid using the given coordinates. We can use the distance formula to find the distance between S and any of the vertices of the base (P, Q, or R). Let's use P:

d(P, S) = sqrt((8-4)^2 + (0-4)^2 + (0-4)^2) = sqrt(16 + 16 + 16) = 4sqrt(3)

Now that we know the slant height, we can use trigonometry to find the angle between two adjacent sides. Let's consider the triangle formed by S, P, and Q (we could also use the triangles with S, Q, and R or with S, R, and P, but we'll get the same answer). We want to find the angle between PQ and QS.

We know that PQ has length 8, and we can use the distance formula again to find the length of QS:

d(Q, S) = sqrt((8-4)^2 + (8-4)^2 + (0-4)^2) = sqrt(16 + 16 + 16) = 4sqrt(3)

Now we can use the sine function:

sin θ = opposite/hypotenuse = PQ/QS

sin θ = 8/4sqrt(3) = 2sqrt(3)/3

θ = arcsin(2sqrt(3)/3) = 54.7° (rounded to the nearest tenth)

Therefore, the answer is A) 54.7°.

Find the Angle,in Degrees,between Two Adjacent Sides of the Pyramid