Question

1. geography a land surveyor wants to measure the distance across a portion of a lake. the surveyor forms the right triangle shown by forming two legs of a right triangle measured on land. what is the distance across the lake? show your work.

20 miles
15 miles

1. a sculpture shaped like a pair of right triangles has leg lengths of 8 feet and 15 feet. what is the length of the hypotenuse of the sculpture?

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle with legs $a$ and $b$, hypotenuse $c$ satisfies $c^2 = a^2 + b^2$.
For question 9: $a=20$ miles, $b=15$ miles
$c^2 = 20^2 + 15^2$

Step2: Calculate squared leg lengths

$20^2 = 400$, $15^2 = 225$
$c^2 = 400 + 225 = 625$

Step3: Solve for hypotenuse (lake distance)

$c = \sqrt{625} = 25$

Step4: Repeat for question 10

Legs $a=8$ ft, $b=15$ ft
$c^2 = 8^2 + 15^2$

Step5: Calculate squared leg lengths

$8^2 = 64$, $15^2 = 225$
$c^2 = 64 + 225 = 289$

Step6: Solve for hypotenuse

$c = \sqrt{289} = 17$

Answer:

1. The distance across the lake is 25 miles.
2. The length of the hypotenuse is 17 feet.