Question

the length of a shadow of a building is 31 m. the distance from the top of the building to the tip of the shadow is 35 m. find the height necessary, round your answer to the nearest tenth.

Explanation:

Step1: Define variables via Pythagoras

Let building height = $h$, shadow = 31 m, hypotenuse = 35 m.
$$h^2 + 31^2 = 35^2$$

Step2: Calculate squared values

Compute $31^2$ and $35^2$.
$$h^2 + 961 = 1225$$

Step3: Isolate $h^2$

Subtract 961 from both sides.
$$h^2 = 1225 - 961 = 264$$

Step4: Solve for $h$

Take square root, round to nearest tenth.
$$h = \sqrt{264} \approx 16.2$$

Answer:

16.2 m