SBMPTN Zone : Balok

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Tipe:

Standar SBMPTN HOTS

No. 1

Balok ABCD.EFGH alasnya persegi dengan AB=4 cm, AE=8 cm. Jika \theta adalah sudut antara bidang ACH dan bidang ABCD, maka \sin\theta =

1. \dfrac45\sqrt2
2. \dfrac23\sqrt2
3. \dfrac12\sqrt2

4. \dfrac47\sqrt2
5. \dfrac13

SKMP Juli 2020

\theta=\angle DOH

BD=4\sqrt2

$\begin{array}{rl}DO& ={\displaystyle \frac{1}{2}}BD\\ & ={\displaystyle \frac{1}{2}}\left(4\sqrt{2}\right)\\ & =2\sqrt{2}\end{array}$

$\begin{array}{rl}HO& =\sqrt{H{D}^2+D{O}^2}\\ & =\sqrt{8^2+{\left(2\sqrt{2}\right)}^2}\\ & =\sqrt{64+8}\\ & =\sqrt{72}\\ & =6\sqrt{2}\end{array}$

$\begin{array}{rl}\sin \theta & ={\displaystyle \frac{HD}{HO}}\\ & ={\displaystyle \frac{8}{6\sqrt{2}}}\\ & ={\displaystyle \frac{4}{3\sqrt{2}}}& \times {\displaystyle \frac{\sqrt{2}}{\sqrt{2}}}\\ & ={\displaystyle \frac{4}{6}}\sqrt{2}\\ & =\boxed{{\displaystyle \boxed{{\displaystyle {\displaystyle \frac{2}{3}}\sqrt{2}}}}}\end{array}$

Jadi, \sin\theta =\dfrac23\sqrt2.
JAWAB: B