Question

1. leland swam from the dock east 26 meters. he turned and swam shown in the diagram below. what is the value of x, the distance leland swam to return to the f 36 m g 24 m h 4 m j 16 m 2. a 10 - foot ladder is leaning against a wall. the bottom of the ladder is 4 feet from the base of the wall, as shown below. which of the following is closest to the distance from the top of the ladder to the base of the wall? a 9 ft b 11 ft c 6 ft d 14 ft

Explanation:

Step1: Apply Pythagorean theorem for problem 1

The right - triangle has sides related by $a^{2}+b^{2}=c^{2}$. Here, assume the two legs of the right - triangle are 10 and 26, and the hypotenuse is $x$. So $x^{2}=26^{2}-10^{2}$. Calculate $26^{2}=676$ and $10^{2}=100$. Then $x^{2}=676 - 100=576$.

Step2: Solve for $x$ in problem 1

Take the square root of both sides of the equation $x^{2}=576$. Since $x>0$, $x = 24$ m.

Step3: Apply Pythagorean theorem for problem 2

For the ladder - wall problem, let the length of the ladder be the hypotenuse $c = 10$ ft and the distance from the base of the ladder to the wall be $a = 4$ ft. Let the height on the wall be $b$. Then $b=\sqrt{c^{2}-a^{2}}$. Calculate $c^{2}=10^{2}=100$ and $a^{2}=4^{2}=16$. So $b=\sqrt{100 - 16}=\sqrt{84}\approx9.17$ ft.

Answer:

1. G. 24 m
2. A. 9 ft