MIP2601 Assignment 3 2025 (Answer Guide) - Due 14 July 2025

MIP2601
Assignment 3 2025
(Answer Guide) -
Due 14 July 2025

QUESTIONS WITH 100%
VERIFIED AND
CERTIFIED ANSWERS.






, 𝑸𝒖𝒆𝒔𝒕𝒊𝒐𝒏 𝟏: 𝑰𝒏𝒅𝒖𝒄𝒕𝒊𝒗𝒆 𝑹𝒆𝒂𝒔𝒐𝒏𝒊𝒏𝒈 [𝟐𝟓 𝒎𝒂𝒓𝒌𝒔]

𝟏. 𝟏 𝑪𝒐𝒏𝒔𝒕𝒓𝒖𝒄𝒕𝒊𝒏𝒈 𝑨𝒏𝒈𝒍𝒆𝒔 𝑼𝒔𝒊𝒏𝒈 𝒂 𝑺𝒕𝒓𝒂𝒊𝒈𝒉𝒕𝒆𝒅𝒈𝒆 𝑶𝒏𝒍𝒚 (𝟐 𝒎𝒂𝒓𝒌𝒔 𝒆𝒂𝒄𝒉)

𝑌𝑜𝑢 𝑎𝑟𝑒 𝑎𝑠𝑘𝑒𝑑 𝑡𝑜 𝒄𝒐𝒏𝒔𝒕𝒓𝒖𝒄𝒕 𝒇𝒊𝒗𝒆 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒕 𝒂𝒏𝒈𝒍𝒆𝒔 (𝟑𝟎°, 𝟒𝟓°, 𝟏𝟎𝟎°, 𝟑𝟎𝟎°, 𝒂𝒏𝒅 𝟔𝟕°)

𝑢𝑠𝑖𝑛𝑔 𝑜𝑛𝑙𝑦 𝑎 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡𝑒𝑑𝑔𝑒 𝑎𝑛𝑑 𝑟𝑒𝑎𝑠𝑜𝑛𝑖𝑛𝑔 — 𝑛𝑜 𝑝𝑟𝑜𝑡𝑟𝑎𝑐𝑡𝑜𝑟. 𝑇ℎ𝑒𝑛 𝑑𝑒𝑠𝑐𝑟𝑖𝑏𝑒 𝑦𝑜𝑢𝑟 𝑟𝑒𝑎𝑠𝑜𝑛𝑖𝑛𝑔

𝑎𝑛𝑑 𝑐𝑜𝑚𝑝𝑢𝑡𝑒 𝑡ℎ𝑒 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑒𝑟𝑟𝑜𝑟 𝑎𝑓𝑡𝑒𝑟 𝑚𝑒𝑎𝑠𝑢𝑟𝑖𝑛𝑔 𝑤𝑖𝑡ℎ 𝑎 𝑝𝑟𝑜𝑡𝑟𝑎𝑐𝑡𝑜𝑟.

𝒂) 𝟑𝟎°

• 𝑹𝒆𝒂𝒔𝒐𝒏𝒊𝒏𝒈: 𝐴 30° 𝑎𝑛𝑔𝑙𝑒 𝑖𝑠 𝑜𝑛𝑒 −
𝑡ℎ𝑖𝑟𝑑 𝑜𝑓 𝑎 90° 𝑎𝑛𝑔𝑙𝑒. 𝐷𝑟𝑎𝑤 𝑎 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑔𝑙𝑒, 𝑡ℎ𝑒𝑛 𝑑𝑖𝑣𝑖𝑑𝑒 𝑖𝑡 𝑖𝑛𝑡𝑜 𝑡ℎ𝑟𝑒𝑒 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒
• 𝑒𝑞𝑢𝑎𝑙 𝑝𝑎𝑟𝑡𝑠 𝑢𝑠𝑖𝑛𝑔 𝑣𝑖𝑠𝑢𝑎𝑙 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑖𝑜𝑛.
• 𝑪𝒉𝒆𝒄𝒌 & 𝑬𝒓𝒓𝒐𝒓: 𝑀𝑒𝑎𝑠𝑢𝑟𝑒 𝑡ℎ𝑒 𝑐𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑒𝑑 𝑎𝑛𝑔𝑙𝑒 𝑤𝑖𝑡ℎ 𝑎 𝑝𝑟𝑜𝑡𝑟𝑎𝑐𝑡𝑜𝑟. 𝐼𝑓 𝑖𝑡 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑠 32°, 𝑡ℎ𝑒𝑛:

𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝐸𝑟𝑟𝑜𝑟 =∣ 32 − 3030 ∣× 100% = 6.67%\𝑡𝑒𝑥𝑡{𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝐸𝑟𝑟𝑜𝑟}
= \𝑙𝑒𝑓𝑡| \𝑓𝑟𝑎𝑐{32 − 30}{30} \𝑟𝑖𝑔ℎ𝑡| \𝑡𝑖𝑚𝑒𝑠 100\%
= 6.67\%𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝐸𝑟𝑟𝑜𝑟 = 3032 − 30 × 100% = 6.67%

𝒃) 𝟒𝟓°

• 𝑹𝒆𝒂𝒔𝒐𝒏𝒊𝒏𝒈: 𝐵𝑖𝑠𝑒𝑐𝑡 𝑎 90° 𝑎𝑛𝑔𝑙𝑒 𝑢𝑠𝑖𝑛𝑔 𝑎 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡𝑒𝑑𝑔𝑒 𝑏𝑦 𝑓𝑜𝑙𝑑𝑖𝑛𝑔 𝑜𝑟 𝑐𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑛𝑔
• 𝑒𝑞𝑢𝑎𝑙 𝑎𝑟𝑐𝑠 𝑜𝑛 𝑡ℎ𝑒 𝑎𝑟𝑚𝑠 𝑎𝑛𝑑 𝑗𝑜𝑖𝑛𝑖𝑛𝑔 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡𝑖𝑜𝑛.
• 𝑪𝒉𝒆𝒄𝒌 & 𝑬𝒓𝒓𝒐𝒓: 𝐼𝑓 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑎𝑠 47°,

𝐸𝑟𝑟𝑜𝑟 =∣ 47 − 4545 ∣× 100% = 4.44%\𝑡𝑒𝑥𝑡{𝐸𝑟𝑟𝑜𝑟}
= \𝑙𝑒𝑓𝑡| \𝑓𝑟𝑎𝑐{47 − 45}{45} \𝑟𝑖𝑔ℎ𝑡| \𝑡𝑖𝑚𝑒𝑠 100\%
= 4.44\%𝐸𝑟𝑟𝑜𝑟 = 4547 − 45 × 100% = 4.44%

𝒄) 𝟏𝟎𝟎°

• 𝑹𝒆𝒂𝒔𝒐𝒏𝒊𝒏𝒈: 𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡 𝑎 90° 𝑎𝑛𝑔𝑙𝑒, 𝑡ℎ𝑒𝑛 𝑎𝑑𝑑 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑙𝑦 10° 𝑣𝑖𝑠𝑢𝑎𝑙𝑙𝑦.
• 𝑪𝒉𝒆𝒄𝒌 & 𝑬𝒓𝒓𝒐𝒓: 𝐼𝑓 𝑟𝑒𝑠𝑢𝑙𝑡 𝑖𝑠 105°,

𝐸𝑟𝑟𝑜𝑟 =∣ 105 − 100100 ∣× 100% = 5%\𝑡𝑒𝑥𝑡{𝐸𝑟𝑟𝑜𝑟}
= \𝑙𝑒𝑓𝑡| \𝑓𝑟𝑎𝑐{105 − 100}{100} \𝑟𝑖𝑔ℎ𝑡| \𝑡𝑖𝑚𝑒𝑠 100\%
= 5\%𝐸𝑟𝑟𝑜𝑟 = 100105 − 100 × 100% = 5%

𝒅) 𝟑𝟎𝟎°

• 𝑹𝒆𝒂𝒔𝒐𝒏𝒊𝒏𝒈: 𝑅𝑒𝑐𝑜𝑔𝑛𝑖𝑧𝑒 𝑡ℎ𝑎𝑡 300° =
𝑓𝑢𝑙𝑙 𝑐𝑖𝑟𝑐𝑙𝑒 (360°) – 60°. 𝐷𝑟𝑎𝑤 𝑎 𝑓𝑢𝑙𝑙 𝑐𝑖𝑟𝑐𝑙𝑒, 𝑡ℎ𝑒𝑛 𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡 𝑎𝑛 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 60° 𝑠𝑙𝑖𝑐𝑒.
• 𝑪𝒉𝒆𝒄𝒌 & 𝑬𝒓𝒓𝒐𝒓: 𝐼𝑓 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑎𝑠 310°,