Answer:sqrt(644)=25.38
The Pythagorean Theorem
If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
This relationship is represented by the formula: [tex]a^{2} +b^{2} = c^{2}[/tex]
[tex]16^{2} +b^{2} =30^{2} ,b=\sqrt{900-256} =\sqrt{644}[/tex]
Answer: The height of the building is 25.38 feet
Step-by-step explanation:
Let AB denote the height of the building.
Let BC denote the distance between the fire truck and the building.
Let AC denote the length of the ladder.
By using the Pythagorean theorem, we have,
AC squared = AB squared + BC squared
Where AC = 30 and BC = 16
Substitute the values that we have,
And you get 30 squared = AB squared + 16 squared
Simplify the terms and we get
900 = AB squared + 256
Subtracting both sides by 256 and we get,
644 = AB squared
Taking the square root on both sides of the equation, we get,
the square root symbol 644 = AB so
There for, the height of the building is 25.38 feet
