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In the regular triangular prism abc-a1b1c1, if all edges are equal in length, then the tangent of the angle between the straight line CB1 and the plane aa1b1b is () A. Root 15 / 3 B. root 15 / 5 C. root 5 / 5 d. root 2
Let CD ⊥ AB be at point D,
∵ plane ABC ⊥ plane aa1b1b
⊥ CD ⊥ plane aa1b1b,
Connect b1d, then ∠ cb1d is the angle between CB1 and plane aa1b1b,
Let the edge length be a, then CD = √ (a ^ 2-A ^ 2 / 4) = √ 3A / 2, b1d = √ (a ^ 2 + A ^ 2 / 4) = √ 5A / 2
∴tan∠CB1D=CD/B1D=√15/5
That is, the tangent of the angle between the straight line CB1 and the plane aa1b1b is √ 15 / 5
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