Question

The following figure shows
`\[\triangle ABC\]` with side lengths to the nearest tenth.

Find

`\[BC\]` in

`\[\triangle ABC\].`
Round to the nearest tenth.


`BC=`

Answer 1

• 10.8

Task :

• To work out the measure of side BC

Solution :

According to the law of sines, the ratio of the length of a side to the sine of the angle opposite to it in a triangle is equal for all the sides and angles in the respective triangle.

The law of sines is given by ,

• 
  `(a)/( \sin(a) ) = (b)/( \sin(b) ) \\`

wherein,

• a and b = sides of the triangle
• sin(a) = angle opposite to side a
• sin(b) = angle opposite to side b

comparing ,

• a = BC
• b = 16
• sin(b) = 180° - (39° + 42°) = 99°
• sin(a) = 42°

plugging in the values in the formula,

• 
  `(16)/( \sin(99) ) = (a)/( \sin(42) ) \\`
• 
  `(16)/(0.987) = (a)/(0.699) \\`
• 
  `0.987a = 16 * 0.669`
• 
  `a = (10.704)/(0.987) \\`
• 
  `a = 10.8`

Thus, the measure of BC is 10.8 .