Determine 8133

Determine the distance between two places, M, and N, between which there is an obstacle so that place N is not visible from place M. The angles MAN = 130°, NBM = 109°, and the distances |AM| = 54, |BM| = 60, while the points A, B, and M lie on one straight line.

Correct answer:

x =  65.3113

Step-by-step explanation:

A=130  B=109  A1=180A=180130=50  B1=180B=180109=71   a=54 b=60  x1 = ba + x2 x2 tan(B1) = x1 tan(A1)  x2 tan(B1) = (b  a + x2) tan(A1)  x2 tan(B1) = (b  a) tan(A1)  + x2 tan(A1)  x2=tanB1tanA1(ba) tanA1=tan71° tan50° (ba) tan50° =tan71° tan50° (6054) tan50° =2.9042111.191754(6054) 1.191754=4.17559  y=x2 tanB1=x2 tan71° =4.1756 tan71° =4.1756 2.904211=12.1268  x=y2+(b+x2)2=12.12682+(60+4.1756)2=65.3113

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