Question

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Answer 1

Answer

Define x and y:

Let x be the height from the ground to the eagle

Let y be the ground distance from the door to the tree

Find the distance when she was at the door:

tanθ = opp/adj

tan(61) = x/y

y = x/tan(61)

Find the distance when she was at the terrace:

tanθ = opp/adj

tan(52) = (x - 4)/y

y = (x- 4)/tan(52)

Solve x:

Both the distance are equal

x/tan(61) = (x- 4)/tan(52)

x tan(52) = (x - 4)tan (61)

x tan (52) = x tan(61) - 4 tan(61)

x tan(61) - x tan(52) = 4 tan(61)

x( tan(61) - tan(52)) = 4 tan(61)

x = 4 tan(61) ÷ ( tan(61) - tan(52) ) = 13.77 m