Question

need help with these two questions ! thanks !

Apply the Law of Sines 7. A helicopter is on a path directly overhead line AB when it is simultaneously observed from locations and B separated by 200 ft. If the angle of elevation from A is 39 and the angle of elevation from Bis 20", what is the distance from cach location to the helicopter? Round to the nearest foot. 200 8. To estimate the height of a building, two measurements are taken. The first measurement shows an angle of elevation to the top of the building as 43°. The second measurement, taken 100 feet closer to the base, yields an angle of elevation of 78°. From these measurements, estimate the height of the building. Round to the ncarest foot

Answer 1

7)

Angle A = 39

Angle B = 20

Angle C = 180 - ( 39 + 20 )

C = 121

Applying law of sines

d1 / sin B = 200 / sin C

d1 = 200 * sin 20 / sin 121

d1 = 80

d2 / sin A = 200 / sin C

d2 = 200 * sin 39 / sin 121

d2 = 147

Distance from location A is 80 feet Distance from location B is 147 feet

8)

h CO 43 X 100 feet

tan 43 = h / ( 100 + x)

tan 78 = h/x

x tan 78 = h

tan 43 ( 100 + x) = h

tan 43 ( 100 + x) = x tan 78

100 tan 43 + x tan 43 = x tan 78

100 tan 43 = x ( tan 78 - tan 43 )

x = 100 tan 43 / ( tan 78 - tan 43 )

x = 24.721279

h = x tan 78

h = 116

Height of the building is 116 feet