sin^2 x + 4 sinx +3 3 + sinx
-------------------------- = -------------------
cos^2 x 1 - sinx
factor the numerator
(sinx +3) (sinx+1) 3 + sinx
-------------------------- = -------------------
cos^2 x 1 - sinx
cos^2 = 1-sin^2x
(sinx +3) (sinx+1) 3 + sinx
-------------------------- = -------------------
1- sin^2x 1 - sinx
factor the denominator
(sinx +3) (sinx+1) 3 + sinx
-------------------------- = -------------------
(1-sinx ) (1+sinx) 1 - sinx
cancel the common term (1+sinx) and (sinx +1)
(sinx +3) 3 + sinx
-------------------------- = -------------------
(1-sinx ) 1 - sinx
reorder the first term
3+sinx 3 + sinx
-------------------------- = -------------------
(1-sinx ) 1 - sinx
Hi there!
Something really good to remember about trigonometry is SOHCAHTOA. I won’t dive into too much detail about it, but you should google it for future assignments.
Anyways,
tan50°=14/AB
ABtan50°=14
AB=14/tan50°
AB=11.75
cos50°=14/AC
ACcos50°=14
AC=14/cos50°
AC=21.78
For the measure of angle C you can use a theorem called the third angle theorem. In every single possible triangle, the sum of all three angles adds up to 180°. You can set up an equation like so...
angleC=180-(90+50)
angleC=180-140
angleC=40°
Since there are 12 inches in 1 foot you have to divide 84 by 12
84 divided by 12 is 7
So, there are 7 feet in 84 inches
