A right pyramid V-EFGH is mounted onto a cuboid ABCDEFGH. Given AB = BC = 15√2 cm, CG = 8 cm, and VG = 17√2…

Question

A right pyramid V-EFGH is mounted onto a cuboid ABCDEFGH. Given AB = BC = 15√2 cm, CG = 8 cm, and VG = 17√2 cm. Calculate: a) The length of AC. b) The angle between the line AG and the plane ABCD.

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Here's the solution to question 11: The figure shows a right pyramid V-EFGH mounted onto a cuboid ABCDEFGH. Given dimensions: AB = BC = 15√(2) cm (This means the base ABCD is a square); CG = 8 cm (Height of the cuboid); VG = 17√(2) cm (Slant edge of the pyramid) a) Calculate the length of AC. Step 1: Identify the shape of the base ABCD. The base ABCD is a square with side length AB = BC = 15√(2) cm. Step 2: Use the Pythagorean theorem in the right-angled triangle ABC. AC² = AB² + BC²; AC² = (15√(2))² + (15√(2))²; AC² = (225 × 2) + (225 × 2); AC² = 450 + 450; AC² = 900; AC = √(900); AC = 30 cm The length of AC is 30 cm. b) The angle between the line AG and the plane ABCD. Step 1: Identify the projection of line AG on the plane ABCD. The projection of point A on plane ABCD is A. The projection of point G on plane ABCD is C (since CG is perpendicular to ABCD). Thus, the projection of line AG on plane ABCD is the line segment AC

A right pyramid V-EFGH is mounted onto a cuboid ABCDEFGH. Given AB = BC = 15√2 cm, CG = 8 cm, and VG = 17√2 cm. Calculate: a) The length of AC. b) The angle between the line AG and the plane ABCD.

Answer

Step-by-step solution

Part a· 2 steps

Identify the shape of the base ABCD.

Use the Pythagorean theorem in the right-angled triangle ABC.

Part b· 1 step

Identify the projection of line AG on the plane ABCD.

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