For the triangle shown find the length AD Assume u 13 v 13

For the triangle shown, find the length AD. (Assume u = 13, v = 13, angle x = 25 degree, and angle y = 25 degree.) AD = A pilot is flying over a straight highway. He determines the angles of depression to two midpoints, 10 mt apart, to be angle x = 35 degree and angle y = 45 degree, as shown in the figure. ()

Solution

u = 13

v = 13

x = 25degrees

y = 25 degrees

applying sine rule in triangle BCD

u / sin x = v / sin C

plugging the values

13 / sin 25 = 13 / sin C

sin C = 13/ 30.760

C = 25 degrees

now angle A = 180 - ( 25+50) = 105 degrees

applying sine rule in triangle CDA

u / sin 105 = AD / sin 25

plugging the values

13/sin 105 = AD / sin 25

AD = 5.69