In the given question,
The tree casts shadow of 25 feet
In the figure, BC show the shadow, such that BC = 25 feet
Angle of elevation from the tip of the shadow is 32 degree
In the figure, Angle ACB = 32 degree, angle of elevation.
and AB represent the length of the tree,
The line AB and BC are making an angle of 90 degree
So, the triangle ABC is a right angle triangle,
From the trignometric ratio of right angle traingle :
Apply the property for the Tangent of an angle : The ratio of the side adjacent to the angle to the opposite side is equal to the tangent of that angle.
[tex]\tan \theta=\frac{Adjacent\text{ Side}}{Opposite\text{ Side}}[/tex]For the angle ACB = 32, Opposite side AB , adjacent side BC = 25
Substitute the value and simplify :
[tex]\begin{gathered} \tan \theta=\frac{Adjacent\text{ Side}}{Opposite\text{ Side}} \\ \tan 32=\frac{25}{AB} \\ AB\text{ = }\frac{25}{\tan 32} \\ AB=\frac{25}{0.62486} \\ AB=40.008 \\ AB\approx40\text{ fe}et \end{gathered}[/tex]Since, AB represent the length of the tree
So, Length of tree = 40 feet
Answer : Height of the tree is 40 feet
