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1. In AABC, L A 40°,a 22 c -40°, a-22 cm, and b-27 cm. Solve for the missing ang

ID: 2920815 • Letter: 1

Question



1. In AABC, L A 40°,a 22 c -40°, a-22 cm, and b-27 cm. Solve for the missing angles to the nearest degree. 2. The light from a rotating offshore beacon (B) can illuminate effectively up to a distance of 250 m. A point on the shore is 500 m from the beacon. From this point, the sight line to the beacon makes an angle of 20° with the shoreline. What length of shoreline, to the nearest metre, A does the beacon effectively illuminate? 500 m 250 m 20° ShorelineC 3. To measure the height, XY, of an inaccessible cliff, a surveyor recorded the data as shown in the diagram. Find the height of the cliff to the nearest tenth of a metre. 36.8 105

Explanation / Answer

1. Using sine law

sin A/a = sin B/b

sin 40/22 = sin B/27

sinB = 27 sin 40/22

B   = 52 degree

C = 180 - A - B = 88 degree

2. sinA/250 = sin C/500

sin 20 / 250 = sin C/500

C = 43.16 degree

B = 180-A-C =116.84 degree

sin A/ 250 = sin B/Shoreline

sin 20/250 = sin 116.84/shoreline

shoreline = 652.2m