The path of a satellite orbiting the earth causes it to pass directly over two tracking stations a and 8, which are 60 mi apart. when the satellite is on one side of the two stations, the angles of elevation at a and b are measured to be 87.0 degree and 84.2 degree, respectively. (round your answers to the nearest mile.)
(a) how far is the satellite from station a?
mi
(b) how high is the satellite above the ground?
mi

(a)  2 miles

 (b)  2 miles

Step-by-step explanation:

Let the distance of the satellite from Station A = |AC|

Let the height of the Satellite from the ground = |DC|

(a) Using size rule on triangle ABC, we can find the value of AC with the following relationship:

|AC|/ Sin 84.2 = 10/ Sin 8.8

|AC| = 10 x (Sin 84.2/Sin 8.8)

         =   10 x 0.1529

        =1.529 miles

        = 2 miles (to the nearest mile)

(b) To calculate the |DC|, we apply the relationship of right-angle triangle ADC:

Sin 87 =   |DC|/ 1.529

|DC|   = 1.529 Sin 87

           = 1.526 miles

           = 2 miles (to the nearest mile)

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