1) The television screen forms a right triangle with the length, width, and diagonal. Using the Pythagorean Theorem:
$a^2 + b^2 = c^2$
$32^2 + w^2 = 40^2$
$1024 + w^2 = 1600$
$w^2 = 576$
$w = \sqrt{576} = 24$
The width of the television screen is 24 inches.
2) The ramp, height, and horizontal distance form a right triangle. Using the Pythagorean Theorem:
$h^2 + d^2 = r^2$
$20^2 + d^2 = 40^2$
$400 + d^2 = 1600$
$d^2 = 1200$
$d = \sqrt{1200} \approx 34.6$
The horizontal distance is approximately 34.6 inches.
3) The tree, distance from Daniel, and kite form a right triangle. Using the Pythagorean Theorem:
$t^2 + d^2 = k^2$
$13^2 + 4^2 = k^2$
$169 + 16 = k^2$
$k^2 = 185$
$k = \sqrt{185} \approx 13.6$
The distance between the kite and Daniel is approximately 13.6 feet.
4) The rope, height of the mast, and distance from the base form a right triangle. Using the Pythagorean Theorem:
$h^2 + 15^2 = 25^2$
$h^2 + 225 = 625$
$h^2 = 400$
$h = \sqrt{400} = 20$
The height of the mast is 20 feet.
5) The ladder, wall, and ground form a right triangle. Using the Pythagorean Theorem:
$l^2 = h^2 + d^2$
$10^2 = h^2 + 5^2$
$100 = h^2 + 25$
$h^2 = 75$
$h = \sqrt{75} \approx 8.7$
The ladder reaches approximately 8.7 feet up the wall.
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem applications worksheet.
