Question

Coconut palm trees can reach heights of up to 100 feet. Suppose you are lying on the beach at a distance of 60 feet from a 48-ft tall palm tree. What is the angle of elevation from your position to the top of the tree? Round to the nearest tenth if necessary.

Answer 1

I think it is 38.7 but im not sure

Answer 2

Use pythagorus to find the length from your position to the top of the palm tree so: 48^2 + 60^2 =x^2
Should get 76.84
Then use the cosine rule to find the angle so the rule is:
C^2 = A^2 + B^2 - (2BC x cos c)
As the angle of elevation is opposite the length of the palm tree C is 48
And because you want the value of c you rearrange to get :
Cos c= A^2 + B^2 - C^2/ 2BC
So you should get Cos c= 0.781 then to find c which is the angle of elevation you do cos^-1 (0.781) =38.65

Or instead of the cosine rule you can use simple trig and use the equation tan^-1 48/60 which also gives the angle = 38.65