Question

The diagram shows a 6 cm x 9 cm x 7 cm cuboid.

7 cm
A
6 cm
B
9 cm
C
a) Find length AC.
Give your answer to 2 decimal places.
b) Find angle ACD.
Give your answer to 1 decimal place.

Answer 1

(a) AC ≈ 10.82 cm

(b) ∠ACD ≈ 32.9°

Explanation:

You want the face diagonal AC and the space angle ACD in the given cuboid with face dimensions 6 cm and 9 cm, and height 7 cm.

Diagonal

The length of the diagonal is found using the Pythagorean theorem.

AC² = AB² +BC²

AC² = (6 cm)² +(9 cm)² = (36 +81) cm² = 117 cm²

AC = √117 cm ≈ 10.82 cm

Length AC is about 10.82 cm.

Angle

The angle of interest has opposite side AD = 7 cm and adjacent side AC ≈ 10.82 cm. The tangent ratio is useful here:

Tan = Opposite/Adjacent

tan(∠ACD) = (7 cm)/(10.82 cm)

∠ACD = arctan(7/√117) ≈ 32.9°

Angle ACD is about 32.9°.

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