Question

Find EF.

Write your answer as an integer or as a decimal rounded to the nearest tenth.

Answer 1

3.0

Explanation:

to find EF, we can use the sine rule. the sine rule states that

`(A)/(\sin a)=(B)/(\sin b)`

where A, B are sides and a,b are angles which are opposite to the sides. so, here the angle 56 degrees is opposite to EF.

first, we need to find the remaining angle as that is opposite to FG. a triangle has 180 degrees and we already know 2 of the 3 angles. let x be the remaining angle.

so,
`90+56+x=180\implies x=180-56-90=34`

so, the angle opposite to FG is 34.

now, we use the sine rule.

`(2)/(\sin34^(\circ))=(EF)/(\sin56^(\circ))`

next, we multiply both sides by sin 56, and then we have

`EF=(2\sin56^(\circ))/(\sin34^(\circ))\approx2.965\approx3.0`

using a calculator.

thus, we have EF is 3.0.