Question - Solving Right-Angled Triangles Using the Pythagorean Theorem
Solution:
The image shows two right-angled triangles that are not drawn to scale. For both triangles, we can use the Pythagorean theorem to solve for the missing side lengths. The Pythagorean theorem states that for a right-angled triangle with sides a, b, and hypotenuse c, the following equation holds true: a^2 + b^2 = c^2.For the first triangle:We need to find the length of the missing side that we'll call a. We have the lengths of the other side (b) and the hypotenuse (c). The hypotenuse is the longest side, which is 5 units, and the other side given is 4 units.Using the Pythagorean theorem, we get:a^2 + 4^2 = 5^2a^2 + 16 = 25a^2 = 25 - 16a^2 = 9a = √9a = 3The length of the missing side is 3 units, corresponding to option B.For the second triangle:The missing side that we need to find is the hypotenuse, which we'll call c. The two sides given are a = 24 units and b = 7 units.Plugging these values into the Pythagorean theorem gives us:24^2 + 7^2 = c^2576 + 49 = c^2625 = c^2c = √625c = 25The length of the missing side, which is the hypotenuse, is 25 units, and this corresponds to option B.So, the answers are:Question 4: B. 3Question 5: B. 25
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