Question

Question #d4a6e

Answer 1

height of the tree is `16.405`metres

Explanation:

Let the ground to be the point `A`
Let the point 32 metres from the left side of the tree to be point`B`
Let the top of the tree to be the point`C`
`ABC` forms a triangle, with side `AB=32`metres
Angle A made by the tree (AC) with AB is `180-94=86` degrees
Angle B made by the line(BC) with AB is `28 degrees`
Angle C made by the line BC with BA is `180-(86+28)=66`degrees
Thus,If `a=BC, b=AC, and c=AB` are the sides of the triangle ABC
and if `A,B, and C` are the angles of the triangle ABC
The sides and angles are connected by the sine rule s

`a/sinA=b/sinB=c/sinC`

`a=?, b=?, c=32` are the sides and
`A=86^@, B=28^@, C=66^@` are the angles

Rewriting the relation so as to determine the length of the tree `b`in terms of the side `c` and the angles `C and B`, we have
`b/sinB=c/sinC`
Substituting

`b/sin28^@=32/(sin66^@)to b=32(sin28^@)/(sin66^@)=16.445`metres

Since `16.445` is inclined at 86^@ degrees to the horizontal,
height of the tree is `(16.445)sin86^@=16.405`metres

height of the tree is `16.405`metres