A math god's answer to glittr's Secondary 3 E Maths Singapore question.
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
Last question use sin rule
Date Posted:
3 years ago
The working can be improved:
① 1.22 is premature approximation. Can be left as exact form.
② it should be AR instead of 1. ER ≠ 1.22 as that is mathematically incorrect.
Writing like that will result in loss of marks.
By sine rule,
sin 45° / AR = sin 60° / RE
Cross multiply,
RE sin 45° = AR sin 60°
RE = AR sin 60° / sin 45°
RE = AR (√3/2) / (1/√2)
RE = √3√2 / 2 AR = √6 / 2 AR
AR = ¼AC → 4AR = AC
RC = AC - AR
= 4AR - AR
= 3AR
RC/RE = (3AR)/(√6 / 2 AR)
= 6/√6
= √6
Since they are similar, and RC and RE are their corresponding sides,
area△BRC / area △ARE
= RC ² / RE ²
= (√6)²
= 6
area of △ BRC
= 6 x area of △ARE
= 6 x 90cm²
= 540 cm²
① 1.22 is premature approximation. Can be left as exact form.
② it should be AR instead of 1. ER ≠ 1.22 as that is mathematically incorrect.
Writing like that will result in loss of marks.
By sine rule,
sin 45° / AR = sin 60° / RE
Cross multiply,
RE sin 45° = AR sin 60°
RE = AR sin 60° / sin 45°
RE = AR (√3/2) / (1/√2)
RE = √3√2 / 2 AR = √6 / 2 AR
AR = ¼AC → 4AR = AC
RC = AC - AR
= 4AR - AR
= 3AR
RC/RE = (3AR)/(√6 / 2 AR)
= 6/√6
= √6
Since they are similar, and RC and RE are their corresponding sides,
area△BRC / area △ARE
= RC ² / RE ²
= (√6)²
= 6
area of △ BRC
= 6 x area of △ARE
= 6 x 90cm²
= 540 cm²
360 Tutoring Program