Question

Please help!! law of sines and cosines related

Answer 1

Answer:

as below

Step-by-step explanation:

to find the height of the pole recall the relationship of sin cos and tan to the triangle with this helpful mnemonic   SOH CAH TOA

Sin = Opp / Hyp

Cos = Adj / Hyp

Tan = Opp / Adj

we will need to solve two triangles and subtract  them.

one is the 15° one of the slope of the road and the other is the 57° one that is the angle of the sun. sooooo,

lets solve the 15° one first.  We are told that the adj side is 75'

since we know the angle and the adj side and we want to find the Opp side let's use Tan b/c it has all of those in it :)  

Tan(15) = Opp / 75

75*Tan(15) = Opp   ( I'll put my calculator to work for this )

20.096 = Opp

that's the height of the road to the bottom of the flag pole along that flag pole axis into the ground  

next lets solve the 57°  triangle in the exact same way

Tan(57) =Opp / 75

75*Tan(57) = Opp

115.4898 = Opp

the tall triangle is the one that goes all the way into the ground,  the small one is the one that is under the ground

so subtract the small one from the big one to find the height of the flag pole above the ground

115.4898-20.096 = 95.3938

so the flag pole is about 95.4 feet tall

:o that's pretty tall :