Answer:
The height of the building is 24m
Step-by-step explanation:
This can be solved using the Pythagorean theorem
which states that the three sides of a right triangle are related by the equation
[tex]c^2 = a^{2} + b^{2}[/tex] (see figure)
where c is the hypotenuse and a, b are the other two sides
Here we have c = the distance from the top of the building to the tip of the shadow = 26m
One side, the length of the shadow ie b = 10 m
So we have
[tex]26^2 = a^2 + 10^2[/tex] where a is the height of the building
Switch sides to get
[tex]a^2 + 10^2 = 26^2[/tex]
[tex]a^2 + 100 = 676[/tex]
Subtract 100 from both sides
[tex]a^2 = 676 - 100 = 576[/tex]
[tex]a = \sqrt{576}[/tex]
a = 24
The height of the building is 24m
