Problem:
In triangle ABC,∠C=90∘,AC=6 and BC=8. Points D and E are on AB and BC, respectively, and ∠BED=90∘. If DE=4, then BD=
Answer Choices:
A. 5
B. 316
C. 320
D. 215
E. 8
Solution:
Because △ABC is a right triangle, the Pythagorean Theorem implies that BA=10. Since △DBE∼△ABC,
BABD=ACDE. So BD=ACDE(BA)=64(10)=320.
OR
Since sinB=BDDE, we have BD=sinBDE. Moreover, BA=10 by the Pythagorean Theorem, so sinB=BAAC=53. Hence BD=3/54=320.
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