急! F5 Trigonometry 11q6

18(a) The distance between A and B.By Sine Formula,
(AB)/sin30^o = (AN)/sin(∠ABN) --∠ABN = 75^o (base ∠s, isos. △)
2AB = 5/sin75^o
AB = 2.59 cm (Correct to 3sig. fig)ORBy Cosine Formula,
AB^2 = AN^2 + BN^2 - 2(AN)(BN)(cos30^o)
AB^2 = 50 - 50cos30^o
AB = 2.59 cm (Correct to 3 sig. fig)(b) The distance between A and C.AC^2 = AB^2 + BC^2 (Pyth. Theorem)
AC^2 = (2.59)^2 + 16
AC = 4.76 cm (Correct to 3 sig. fig)(c) The angle θ.In ΔABC,
AC^2 = 10^2 + 4^2 (Pyth. Theorem)
AC = 2√29 cmBy Cosine Formula,
AC^2 = AM^2 + CM^2 - 2(AM)(CM)(cosθ)
4.76^2 = 29 + 29 - (58)cosθ -- AM = CM (Intercept Theorem)
cosθ = 0.609 (Correct to 3 sig. fig)
θ = 52.5^o -- θ = 307^o and other greater values are rejected19(a) Length of ST.ST^2 = 15^2 + 20^2 (Pyth. Theorem)
ST = 25 cm(b) The distance betweem T and M.
MT^2 = ST^2 - SM^2 (Pyth. Theorem)
MT^2 = 625 - 49 -- M is the mid-point of SR (given) where SR = 14cm (property of rectangle)
MT = 24 cm(c) The angle between TS and PQT.Let θ be the required angle,
tanθ = 15/20 -- The requied angle actually is ∠STP
θ = 36.9^o (Correct to 3 sig. fig)(d) Angle between RST and PQRS.The required angle
= 90^o - 36.9^o (∠sum of △) --The requied angle actually is ∠PST
= 53.1^o (Correct to 3 sig. fig)(e) Angle between PST and PQRS.Let Φ be the required angle,
By Cosine Formula,
20^2 = 20^2 + 14^2 - 2(20)(14)(cosΦ) --The requied angle actually is ∠QPT
cosΦ = 0.35
Φ = 69.5^o (Correct to 3 sig. fig)

2013-01-16 07:50:38 補充：
不斷打錯了"required"...