Answer:
h ≈ 30.10 ft
Step-by-step explanation:
Marie measures the angle of elevation from a point A to a tree as 34° . She works 10 ft directly towards the tree and discovered the new angle of elevation is 41°. The height of the tree can be computed below.
let
a = distance from point B to the tree
h = height of the tree
The right angle triangle formed from point B, we can use tan to find the height of the tree.
tan 41° = opposite /adjacent
tan 41° = h/a
cross multiply
h = a tan 41°
The right angle formed from point A
tan 34° = opposite/adjacent
tan 34° = h/(a + 10)
(a + 10)tan 34° = h
Therefore,
a tan 41° = (a + 10)tan 34°
0.8692867378
a = 0.6745085168(a + 10)
0.8692867378a = 0.6745085168a + 6.7450851684
collect like terms
0.8692867378a - 0.6745085168a = 6.7450851684
0.194778221a = 6.7450851684
a = 6.7450851684/0.194778221
a = 34. 629565532 ft
height of the tree can be find with
h = a tan 41°
h = 34. 629565532 × 0.8692867378
h = 30.103022053 ft
h = 30.10 ft
