Question

There is a small island in the middle of a 100 meter wide river and a tall tree stand on the island p and q are the points directly opposite to each other on the two banks and in line with the tree. If the angle of of evelation of the top of the tree from p and qare 30 and 40 drgee. Find the height of the tree

Answer 1

Answer:

34.189 m

Step-by-step explanation:

let L distance from base of tree to q bank

tan 40=h/L

h=L x tan40 .................1

tan 30 = h/(100-L)

h=(100-L) tan30 ..........2

equating both

0.839 L= 0.577 (100-L)

1.416L= 57.7

L= 40.75 m

h= 0.839L=0.839x40.75= 34.189 m

Height of tree is 34.189 m

Answer 2

Answer:

34.2 m

Step-by-step explanation:

Define x:

Let h be the height of the tree

Define d:

Let d be the distance of of P to the foot of the tree

P:

tan(θ) = opp/adj

tan(30) = h/d

h= dtan(30)

Q;

tan(θ) = opp/adj

tan(40) = h/(100 - d)

h= (100 - d)tan(40)

Solve d:

dtan(30) = (100 - d)tan(40)

dtan(30) = 100tan(40) - dtan(40)

dtan(30) + dtan(40) = 100tan(40)

d(tan(30) + tan(40)) =100tan(40)

d = 100tan(40) ÷ (tan(30) + tan(40))

d = 59.24m

Find the height:

h= dtan(30)

h = 59.24 x tan(30)

h = 34.2 m

Answer: The height is 34.2 m