Question

Q6

4 pts) In each of the following, two sides and an angle of a triangle are given. Assume a 'pposite side a, ß is opposite side b, and y is opposite side c. Determine whether the giv nformation results in two triangles, one triangle, or no triangle at all. Clearly show how he Law of Sines to answer the question. You don't need to solve the triangles. a) b= 14,c = 23, B = 82° b) a = 4.5,c=7,a = 23°

Answer 1

In first part the value of sine resulting greater than 1 which is not possible as value of sine lies between -1&1 hence No Triangle Exists.

[a] SOLUTION 8 b= 14, using Law C'= 23, B = 82° of sines b C Sinß sinr 14 23 sing2 sinr Siar = 23.sin 82 n 1.62 T4 Here sinra 1.62 but we Show value of sine lies between -le sinrsi and here sinr> Hence No Triangle Exists for the given data. SOLUTION [6] a ² 4.5, c=7 2=230 с sind Sinr sinr- c. sind Siny a I sin23° 10.60 4.5 8- Sin' (0.60) a 36° but we know aw obtuse angle is the sine of its suppliment » sin 36° = sin 1440 Hence Two distinct Triangles Exist. 30 23 7 36 23 Tuy

In part b) angle corresponding to c=7 is resulting in 36 degree and sine value of 36 degree and 144 degree are same and validate the sum of interior angle of triangle hence Two distinct triangles exist.