Trigonometry Word Problem

Question

a distance from tree the angle of elevation is 44 degrees to the top of tree. moves 70m away angle of elevation to top of tree is 25 degrees. Height of tree?

Answer 1

Let h be the height of the tree and x the distance when the angle was 44°.

 

tan(44) = h/x => h = x * tan(44)

 

When the angle of elevation is 25°, the distance from the tree is x + 70

 

tan(25) = h/(x + 70) =  x * tan(44)/(x + 70)

(x + 70)tan(25) = x * tan(44)

x * tan(25) + 70 * tan(25) = x * tan(44)

x * (tan(44) - tan(25)) = 70 * tan(25)

x = 70 * tan(25)/(tan(44) - tan(25))

 

Then h = x * tan(44) = 70 * tan(25) * tan(44)/(tan(44) - tan(25))

 

Evaluate these values and get the height and initial distance from the tree.

 

h = 63.121 m and x = 65.364 m

 

 

Answer 2

t represents the height of the tree

x represents the distance form the tree to the point of 44° elevation

 

tan 44° = t / x ⇒ x tan 44°

tan 25° = t / (x + 70) ⇒ (x + 70) tan 25° = t

 

x tan 44° = (x + 70) tan 25°

 

Solve for x, then solve for t.