From a distance of 200 m, Susan looks up at the top of a lighthouse. The angle of elevation is 9°. Her eyes are 1.22 m above the ground. Determine the height of the lighthouse to the nearest meter. * 37.2 m
32.7 m
32.9 m
22.6 m

these are triangle problems, they are difficult unless you keep in mind that there is an invisible triangle and you use the Mnemonic SOH CAH TOA to keep sin, cos, and tan,  straight..

Step-by-step explanation:

what do we know about the imaginary triangle that is being made from Susan to the lighthouse?  that from Susan's feet  to the lighthouse base is 200 m  so that side of the imaginary triangle is 200 meters.. got it... Susan's eyes are 1.22 meters up   and that her angle of looking up at the top of the lighthouse is 9 degrees.. okay .. we have enough info to solve this.  B/c we have an angle and also the adjacent ( next to )  side to that angle  , great

B/c we have the adjacent side and the angle.. and we want to know the Opposite side.. which will be the height of the light house,  use one of the SOH CAH TOA formulas for those three pieces of info in it.. I see that that TOA has all of those.  Tan(Ф)= Opp / Adj  

Tan(Ф) is our angle

Opp is the Opposite side that we want to find

Adj is the Adjacent side that we know.. 200

Tan(9)=Opp / 200

use algebra to rearrange our formula

Tan(Ф)*Adj = Opp

Tan(9)*200 = Opp

I'll use my calculator to figure out what tan(9) is b/c I don't have that memorized :P and multiply that by 200

31.677 m

Also.. b/c we just figured out the triangle from  Susan's eyes to the lighthouse.. we have to add her eye height off the ground to our answer

31.677+1.22= 32.897

yeah   32.9     looks like the right answer