Math Problem Statement

Figure 2 shows a right pyramid ABCDO with a horizontal square base of side 8 cm. The vertical height of the pyramid is h cm and OA = OB = OC = OD = 12 cm. Find the exact value of h and solve the other parts as described in the image.

Solution

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Math Problem Analysis

Mathematical Concepts

Geometry
Right Pyramid
Angles in 3D Shapes
Vector Mathematics

Formulas

Pythagoras' theorem: a^2 + b^2 = c^2
Trigonometric ratios: cosθ = adjacent/hypotenuse
Distance formula for vectors: |PQ| = √[(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2]

Theorems

Pythagoras' Theorem
Properties of right pyramids
Trigonometric angle properties

Suitable Grade Level

Grades 10-12

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