Topic 2: Pythagorean Theorem Skills Practice

Question-and-answer flashcards with complete step-by-step solutions for real-world word problems applying the Pythagorean Theorem.

According to Problem 15, if the distance from your feet to the base of a cliff is $23\text{ feet}$ and the distance from your feet to the top of the cliff is $26\text{ feet}$, what is the height of the cliff to the nearest hundredth of a foot?

The height of the cliff is approximately $12.12\text{ feet}$, calculated as $\sqrt{26^2 - 23^2} = \sqrt{676 - 529} = \sqrt{147} \approx 12.12\text{ feet}$.

According to Problem 16, if you are standing $17\text{ feet}$ from the base of a flagpole that is $9\text{ feet}$ tall, what is the distance from your feet to the top of the pole to the nearest hundredth of a foot?

The distance is approximately $19.24\text{ feet}$, calculated as $\sqrt{17^2 + 9^2} = \sqrt{289 + 81} = \sqrt{370} \approx 19.24\text{ feet}$.

According to Problem 17, if a door frame has a width of $36\text{ inches}$ and a diagonal length of $96\text{ inches}$, what is the height of the door frame to the nearest inch?

The height of the door frame is approximately $89\text{ inches}$, calculated as $\sqrt{96^2 - 36^2} = \sqrt{9216 - 1296} = \sqrt{7920} \approx 89\text{ inches}$.

According to Problem 18, if a swing bar is $8\text{ feet}$ from the ground and the base of the support beam extends $3\text{ feet}$ from the plane of the swing bar, how long should each support beam be to the nearest tenth of a foot?

Each support beam should be approximately $8.5\text{ feet}$ long, calculated as $\sqrt{8^2 + 3^2} = \sqrt{64 + 9} = \sqrt{73} \approx 8.5\text{ feet}$.

According to Problem 19, if a streetlamp is $12\text{ feet}$ high and Clayton places the base of his ladder $4\text{ feet}$ from the base of the streetlamp, how long must the ladder be to reach the top to the nearest hundredth of a foot?

The ladder must be approximately $12.65\text{ feet}$ long, calculated as $\sqrt{12^2 + 4^2} = \sqrt{144 + 16} = \sqrt{160} \approx 12.65\text{ feet}$.

According to Problem 20, if a basketball hoop is $10\text{ feet}$ high and Perry places his ladder $4\text{ feet}$ from the base of the hoop, how long must the ladder be to reach the hoop to the nearest hundredth of a foot?

The ladder must be approximately $10.77\text{ feet}$ long, calculated as $\sqrt{10^2 + 4^2} = \sqrt{100 + 16} = \sqrt{116} \approx 10.77\text{ feet}$.

According to Problem 21, if Chen wants the end of a ramp to extend $4\text{ feet}$ from its base and the base is $18\text{ inches}$ high, how long should the piece of wood for the ramp be to the nearest tenth of an inch?

The piece of wood should be approximately $51.3\text{ inches}$ long, calculated by converting $4\text{ feet}$ to $48\text{ inches}$: $\sqrt{48^2 + 18^2} = \sqrt{2304 + 324} = \sqrt{2628} \approx 51.3\text{ inches}$.