Use the law of sines to solve the given problem. A small island is approximately a triangle in shape. If the longest side of the island is 550 m, and two of the angles are 30degrees and 50degrees, what is the length of the shortest side?

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Favouredlyf Favouredlyf · Answer 1 · 2019-12-07T10:57:41+01:00

Answer: the shortest side is 279.24 feet

Step-by-step explanation:

The diagram of the triangle in shown in the attached picture. The given angles of 30 degrees and 50 degrees are for the shorter sides.

Since the sum of angles in a triangle is 180 degrees, it means that the angle of the longer side, x will be

x = 180 - (30 + 50)

x = 180 - 80 = 100 degrees

The sine rule states that

a/sinA = b/sinB = c/sinC

c = 550

a = the shortest side.

Therefore

a/sinA = c/ sinC

a/sin30/= 550/sin100

asin100 = 550sin30

0.9848a = 550×0.5 = 275

a = 275/0.9848

a = 279.24 feet