My Math Question

Question

To Calculate the height of a tree, Marie measures the angle of elevation from a point A to be 34. She then walks 10 feet directly towards the tree, and finds the angle of elevation from the new point B to be 41. What is the height of the tree.

Answer 1

Let x be the distance from point B to the tree

h = height of tree

 

h/(10 + x) = tan34° ≅ 0.6745 ⇒ h = 0.6745(10 + x) = 6.745 + 0.6745x 

x = (h - 6.745) / 0.6745

 

h/x = tan41° ≅ 0.8693 ⇒

x = h/0.8693 ≅ 1.150h

 

Combine the 2 equations above for x and get

 

1.150h = (h - 6.745) / 0.6745

 

0.7757h = h - 6.745

 

h(1 - 0.7757) = 6.745

 

h ≅ 30.07 ft