Question

1. a rope from the top of a mast on a sailboat is attached to a point 19 feet from the mast. if the rope is 28 feet long, how tall is the mast? round to the nearest tenth of a foot. 47.0 feet 20.6 feet 23.1 feet 33.8 feet

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the mast be \(h\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 28\) (length of the rope, hypotenuse) and \(a=19\) (distance from the mast). We need to find \(b\) (height of the mast), so \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 28\) and \(a = 19\) into the formula: \(b=\sqrt{28^{2}-19^{2}}=\sqrt{(28 + 19)(28-19)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). Then \(b=\sqrt{47\times9}=\sqrt{423}\).

Step3: Calculate the square - root

\(\sqrt{423}\approx20.6\) (rounded to the nearest tenth).

Answer:

20.6 feet