Respuesta :
The height of buliding is 14.2 feet.
How to find the height of the building?
given that
A student standing on top of a building sees a flying bird that is 25 feet away and 20 feet above the top of the building.
The student also sees a car on the ground at an angle of depression of 70.
angle of depression is 70°.
Let the height of buliding is X.
Here we need to discover the peak of the building, the step is to discover the horizontal distance among the student and the car.
we already know that one side and hypothesis of the triangle.
so find other side by using phythagoreous theorem.
[tex] {s}^{2} + {s}^{2} = {h}^{2} \\ {20}^{2} + {s}^{2} = {25}^{2} \\ {s}^{2} = {25}^{2} - {20}^{2} \\ {s}^{2} = 625 - 400 \\ {s}^{2} = 225 \\ s = \sqrt{225} \\ s = 15[/tex]
the horizontal distance among the student and the car is 15 feet.
To find the height of buliding using tan ratio
[tex]tan(θ) = \frac{opposite \: side}{adjacent \: side} \\ tan(70) = \frac{x}{15} \\ tan(70) \times 15 = x \\ x = 14.2feet[/tex]
Hence the height of buliding is 14.2 feet.
Learn more about problems on height of buliding,refer:
https://brainly.in/question/49720412
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