Answer:
(a) AC ≈ 10.82 cm
(b) ∠ACD ≈ 32.9°
Step-by-step 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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