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
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