what is the missing length?
what is the missing length?
Answer
Explanation:
Step1: Apply Pythagorean theorem
Let the length of the ladder be the hypotenuse (c = 50) ft and the base - distance be (a = 35) ft. The Pythagorean theorem is (a^{2}+b^{2}=c^{2}), where (b) is the height we want to find. So, (b^{2}=c^{2}-a^{2}).
Step2: Substitute values
Substitute (c = 50) and (a = 35) into the formula: (b^{2}=50^{2}-35^{2}=(50 + 35)(50 - 35)) (using the difference - of - squares formula (x^{2}-y^{2}=(x + y)(x - y))). Then (b^{2}=(85)(15)=1275). So, (b=\sqrt{1275}\approx35.71) ft.
Answer:
Approximately (35.71) ft