The formula for the length of the hypotenuse in a right triangle is sqrt(a^(2)+b^(2)) where a and b are the lengths of the triangle's sides (this formula is derived from the Pythagorean theorem). From the side, a certain ramp has a right-triangular shape. Its height is 30 centimeters and its horizontal length is 3 meters. What calculation will give us the estimated length of the ramp in meters? Choose 1 answer: (A) sqrt((30^(2))/(100^(2))+3^(2)) (B) sqrt(30^(2)+3^(2)*100^(2)) (C) sqrt(30^(2)*100^(2)+3^(2)) (D) sqrt(30^(2)+(3^(2))/(100^(2)))

Question

The formula for the length of the hypotenuse in a right triangle is  sqrt(a^(2)+b^(2)) where  a and  b are the lengths of the triangle's sides (this formula is derived from the Pythagorean theorem). From the side, a certain ramp has a right-triangular shape. Its height is 30 centimeters and its horizontal length is 3 meters. What calculation will give us the estimated length of the ramp in meters? Choose 1 answer: (A)  sqrt((30^(2))/(100^(2))+3^(2)) (B)  sqrt(30^(2)+3^(2)*100^(2)) (C)  sqrt(30^(2)*100^(2)+3^(2)) (D)  sqrt(30^(2)+(3^(2))/(100^(2)))

Bytelearn · Accepted Answer

Convert to meters: First, we need to convert all measurements to the same unit. Since we want the answer in meters, we will convert the height from centimeters to meters. Height in meters = Height in centimeters ÷ 100 Height in meters = 30 cm ÷ 100 Height in meters = 0.3 mApply Pythagorean theorem: Now, we have the height (a) as 0.3 meters and the horizontal length (b) as 3 meters. We can apply the Pythagorean theorem to find the length of the hypotenuse (c), which is the length of the ramp. The formula is c = sqrt(a^2 + b^2).Substitute values: Substitute the values of a and b into the formula. c = sqrt((0.3)^2 + (3)^2) c = sqrt(0.09 + 9) c = sqrt(9.09)Evaluate square root: Now, we evaluate the square root to find the length of the ramp. c = sqrt(9.09) c ≈ 3.01 meters

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