Subjects geometry

Triangle Gradient

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Triangle Gradient


1. The problem states we have a right-angled triangle with sides 9 m, $\sqrt{4819}$ m, and a hypotenuse of 70 m. We need to find the gradient of the hypotenuse (70 m line) as a percentage. 2. Recall that the gradient (slope) is given by the ratio of the "rise" over the "run." For a right triangle, if we consider the 70 m hypotenuse as the diagonal, the gradient relative to the horizontal side (run) is the vertical side (rise) divided by the horizontal side (run). 3. We identify the two legs: one is 9 m, and the other is $\sqrt{4819}$ m. We will take the horizontal leg as 9 m and the vertical leg as $\sqrt{4819}$ m. 4. Calculate $\sqrt{4819}$. We approximate: $$\sqrt{4819} \approx 69.44$$ 5. Thus the gradient is: $$\text{gradient} = \frac{\text{rise}}{\text{run}} = \frac{69.44}{9} \approx 7.716$$ 6. To express the gradient as a percentage, multiply by 100: $$7.716 \times 100 = 771.6\%$$ 7. Therefore, the gradient of the 70 m hypotenuse line is approximately $771.6\%$. Final answer: The gradient is approximately **771.6%**.