Answer:
this is a Sin(), Cos() and Tan() function problem. use the Mnemonic (new-monic) SOH CAH TOA (soo caw tow ah ) to remember which function sin() cos() or tan() to use.. :) these types of problems are pretty confusing, Use that Mnemonic to keep the functions in order
Explanation:
since we know the distance to the tree.. and we know the angle and we have a formula TOA to figure out the one pieces of info we don't know ... use TOA that tells us our formula.. TOA(Ф)=Opp / Adj where Tan(Ф) is using Ф= to our angle of 32 degrees ( remember Ф can be in degrees or radians, its in degrees for this problem) Adj = the Adjacent side of the triangle from the known angle.. the 32 degree angle , Opp = the Opposite side of the triangle formed by the imaginary lines from Kari to the base of the tree and from Kari to the top of the tree.. and then the tree , from it's base to it's top... we know the angle and the Adj side of that triangle so we can figure out that last part of TOA by saying Tan(Ф)=Opp/ Adj .... or say Tan(32)= Opp / Adj ⇒ Tan(32)=Opp / 90 ⇒ Tan(32) *90 = Opp this will be the height from the ground to the top of the tree.. but.. the tree is at an angle , keep in mind... sooo Tan(32)*90=56.238 feet now take the new triangle that we know one side to... from the ground to the height of the tree.. in a vertical line from the ground to a point at 56.238 feet .. that is the Adj side of this new triangle.. the tree is on the Hypotenuse of this new trialge, which we want to find. we know the Adj side we know the angle to find the Hypotenuse use CAH , from our Mnemonic at the top, the Mnemonic is really important b/c keeping track of which part goes where in the triangles is pretty confusing. Cos(5)=Adj / Hyp ⇒ Cos(5)=56.238 / Hyp ⇒56.238 / Cos(5)= Hyp = 56.453 feet :) that's how tall that tree is , lets chop it down :P and blame it on George Washington :P The tree, to the nearest 10th of a foot, is 56.5 feet