Question

In triangle DEF, `m/_D = 44°, m/_E=61°,` and `EF=20` `i n`. What is `DE` to the nearest tenth of an inch?

Answer 1

`DE=27.8" inches to the nearest tenth of an inch"`

Explanation:

`"using the "color(blue)"sine rule"`

`color(red)(bar(ul(|color(white)(2/2)color(black)((DE)/sinF=(EF)/sinD=(DF)/sinE)color(white)(2/2)|)))`

`angleF=180-(61+44)=75^@`

`rArr(DE)/(sin75^@)=20/sin44^@`

`rArrDE=(20xxsin75^@)/sin44^@`

`color(white)(rArrDE)~~ 27.8" inches"`