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Introduction:

Introduction: We used the internet explorer to find triangles which do not exist in the real world but they do on the map at least on ours. The map hasn’t giving us full information. Once the map missed an angle and once it has missed a side.

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Introduction:

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  1. Introduction: • We used the internet explorer to find triangles which do not exist in the real world but they do on the map at least on ours. • The map hasn’t giving us full information. • Once the map missed an angle and once it has missed a side. • Anyhow we had to use the law of cosines and the law of sine to find the missing angle / side.112

  2. On the 1st triangle • On the 1st triangle the picture shows a triangle formed by 3 emirates which are located in the Untied Arab Emirates. • The picture was taken from Google earth and the angles and sides are pin-point accurate. The 3 emirates had a great past especially Dubai will it started as a main port in the gulf and look at it now… • The other 2 emirates are RAK and Fujairah, RAK stands for Ras Al Khaimah, Fujairah had a busy past a very recent one with the protégés when they invaded them and finally it has been set free since that time.

  3. 1- Find angle (R) by using the law of cosines: because we have three sides and we want to find one angle. r2= d2+f2– 2(d)(f) Cos(R) 1312= 922+ 862 – 2(92)(86) Cos(R) 1312 – 922 – 862= –15824Cos(R) 1301= –15824Cos(R) 1301/(-15824)= -15824Cos(R) Cos(R)= -0.08221= Cos-1(-0.08221) (R)≈ 95° 3- Find angle (D):- D= 180 – (95+41) = 44° D = 44° 2- Find angle (F) by using the law of Sins, to find the other angles. Sin(F)/f = Sin(R)/r Sin(F°)/86 = Sin(95°)/131 Sin(F)= 86 Sin(95°) / 131= 0.65399 Sin(F)= Sin-1(0.65399) ≈ 41° (F) ≈ 41° 4- The area of the triangle:- Area=½(86)(92)Sin(95) Area≈ 3941 km2

  5. On the 2nd triangle • As we mentioned before the details are pin-point accurate and the information were taken from Google Earth. • Anyhow on this triangle the 3 points That were chosen are capital cities of 3 different countries which are SaudiaArabia, Kuwait, and Bahrain. • The 1st one Riyadah used to be a deserted small city in the middle of the desert but due to amazing leadings and developments the city has became something truly astonishing. • The 2nd is Kuwait City which is obviously the capital of Kuwait it has the recognizable tower which required modern architecture although it was made a long time ago. And not to mention Manamah it was a pretty much nothing until oil wealth helped the super fast growth of Bahrain.

  6. 1- Find angle (K) by using the law of cosine, because we have three sides. Sin(K)/k = Sin(M)/m Sin(K)/486 = Sin(66°)/707 486 Sin(66°) / 707 = 0.62798 K= Sin-1(0.62798) ≈ 39° Medina 2- Find angle (R) by using the law of sines, because we have two sides and an angle opposite on of them. Sin(39)/486 = Sin(R)/474.5 474.5 Sin(39)/486 = 0.6144 Sin-1(0.6144)≈ 38° 4- Find the area of the triangle:- Area= ½ (k)(m)sin(R) Area = ½ (486)(707)sin(38°) Area = 171801 sin(38°) Area= 105771.25km2 3- Find angle (M) by subtract (R) and (K) from 180°. M= 180 – (39+38) = 103°

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