Mathematics 10 — Exercise Review · Q4 (ii)

Full question

Cuboid ABCDEFGH has AB = 5 cm, BC = 7 cm and AE = 3 cm. Find the angle between diagonal AG and the base ABCD.

Step-by-step solution

1. The projection of AG onto the base is AC=√74; vertical height is CG=3.

2. Calculate this operation before combining the remaining terms.

   $$\frac{1}{\sqrt{74}}=\frac{1}{74}\times \sqrt{74}$$

3. Calculate this operation before combining the remaining terms.

   $$3\times \frac{1}{74}\times \sqrt{74}=\frac{3}{74}\times \sqrt{74}$$

4. Use tanθ=CG/AC=3/√74.

   $$\frac{3}{\sqrt{74}}$$

5. Take inverse tangent in degrees.

   $$19.225856$$

6. Round to one decimal place.

Answer

The final answer is shown below.