Pergunta

The sides of a triangle are 30,64, and 90 Use the Pythagorean Theorem to determine if the triangle is right, acute or obtuse. Answer Attemptiout of 2 The triangle is square because the square of the largest side square the sum of the squares of the other two sides.
Solução

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Beatriz MariaProfissional · Tutor por 6 anos
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The triangle is obtuse because the square of the largest side (90) is greater than the sum of the squares of the other two sides (4996).
Explicação
## Step 1<br />The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as:<br />### \(a^2 + b^2 = c^2\)<br />where \(c\) is the hypotenuse and \(a\) and \(b\) are the other two sides.<br /><br />## Step 2<br />In this problem, the sides of the triangle are 30, 64, and 90. We need to determine if the triangle is right, acute, or obtuse.<br /><br />## Step 3<br />First, we need to identify the largest side, which is 90. This will be our hypotenuse.<br /><br />## Step 4<br />Next, we calculate the squares of the other two sides:<br />### \(30^2 = 900\)<br />### \(64^2 = 4096\)<br /><br />## Step 5<br />Then, we add these two results together:<br />### \(900 + 4096 = 4996\)<br /><br />## Step 6<br />Finally, we compare this sum to the square of the hypotenuse:<br />### \(90^2 = 8100\)<br /><br />## Step 7<br />Since \(4996 < 8100\), the sum of the squares of the other two sides is less than the square of the hypotenuse. This means that the triangle is obtuse.
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