An observer

An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?

Correct answer:

y =  35.3553 m

Step-by-step explanation:

A=45  B=30  x3=50 m  tan A = y : x1 tan B = y : x2  x22=x32+x12=502+35.35532=2500   y = x1   tan A = x2   tan B   x1   tan A = x2   tan B x12   tan2 A = x22   tan2 B  x12   tan2 A = (x32+x12)   tan2 B  t1=(tanA)2=(tan45° )2=12=1 t2=(tanB)2=(tan30° )2=0.577352=0.33333  x12   t1 = x32   t2 +x12   t2 x12   (t1t2)  = x32   t2  x1=x3 t1t2t2=50 10.33330.3333=25 2 m35.3553 m  y=x1 t1=35.3553 1=25 235.3553 m   Verifying Solution:  x2=y/t2=35.3553/0.3333=25 6 m61.2372 m  x22=x32+x12=502+35.35532=25 6 m61.2372 m

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