Question

Really simple triangle question! please help!

Answer 1

see explanation

Explanation:

Nicole has the correct equation

To find ∠ F use the Sine rule, that is

The ratio of the sine of an angle to the side opposite is equal to the ratio of the sine of another angle to the side opposite.

Matthew and Leah have mixed up the sine of an angle with the incorrect opposite side.

Following on with Nicole's solution

`(sin100)/(27)` =
`(sinF)/(19)` ( cross- multiply )

27 × sinF = 19 × sin100° ( divide both sides by 27 )

sinF =
`(19sin100)/(27)` ≈ 0.6930, thus

F =
`sin^(-1)` (0.6930 ) ≈ 43.9° ( to 1 dec. place )