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小 發表於 2016-12-15 02:30 PM (第 2682 天)
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(i) In Figure 5(a), clearly AM = BM. Therefore, in Figure 5(c), triangles ACM and BCM are congruent (SSS), which implies angle ACM = angle BCM. Now we can use SAS to prove that triangles ACR and BCR are congruent.
This means that AR = BR can be calculated, so you can use Pyth. thm. to calculate AB. Now apply cosine law to triangle ABN to find angle ANB.
(ii) Applying cosine law to triangle AMR gives
tan(ABR) = [AM2 + MR2 - 2 x AM x MR x cos(AMC)]1/2 / BR.
Note that AM, MR and BR are constant. When angle AMC decreases (from 90 degrees to 0 degree), cos(AMC) increases, so tan(ABR) decreases from the above formula, and hence angle ABR decreases.
[ 本帖最後由 tamgary 於 2016-12-16 04:36 AM 編輯 ]
