Answer:
8.2 m
Step-by-step explanation:
You want the length of the shadow whose tip is 34 m from the top of a 33 m building.
Hypotenuse
The described geometry can be modeled by a right triangle with one leg 33 m and hypotenuse 34 m. The Pythagorean theorem tells us the length of the other leg is ...
a² +b² = c²
b² = c² -a²
b = √(c² -a²)
b = √(34² -33²) ≈ 8.2 . . . . meters
The length of the shadow is about 8.2 meters.
__
Additional comment
The angle of elevation to the top of the building can be found from the trig relation ...
Sin = Opposite/Hypotenuse
And the length of the shadow can be found from the relation ...
Cos = Adjacent/Hypotenuse
If α is the angle of elevation, then ...
sin(α) = 33/34 ⇒ α = arcsin(33/34)
and
Adjacent = Hypotenuse × cos(α)
Adjacent = 34·cos(arcsin(33/34)) ≈ 8.2 . . . . meters
where the "adjacent" side of the triangle is the side between the building and the tip of the shadow, along the ground.
