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frutty [35]
3 years ago
15

Find the measures of the acute angles of the right triangle shown

Mathematics
1 answer:
yanalaym [24]3 years ago
7 0

9514 1404 393

Answer:

  • 2x° = 64°
  • (x-6)° = 26°

Step-by-step explanation:

The acute angles in a right triangle are complementary:

  2x° +(x -6)° = 90°

  3x = 96 . . . . . . . . . divide by °, add 6

  x = 32 . . . . . . . . . divide by 3

  (x-6)° = (32 -6)° = 26°

  2x° = 2(32)° = 64°

The acute angles have measures 26° and 64°.

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Smallest of 3 consecutive positive intergers if the product of the smaller two intergers is 5 less than 5 times the largest inte
amm1812

What a delightful little problem ! (Partly because I could see
right away how to do it, and had the answer in a few minutes,
after a lot of impressive-looking algebra on my scratch-paper.)

Three consecutive integers are . . . x,  x+1,  and  x+2

The smallest two are . . . x  and  x+1
    Their product is . . . . . x(x+1)

5 times the largest one is . . . 5(x+2)
      5 less than that is . . . . . . 5(x+2)-5

Now, the conditions of the problem say that    <u>x (x + 1) = 5 (x+2) - 5</u>
THAT's the equation we have to solve, to find 'x' .

       Eliminate parentheses:    x² + x = 5x + 10 - 5
            Combine like terms:    x² + x = 5x + 5
Subtract 5x from each side:    x² - 4x = 5
Subtract  5  from each side:   <u>x² - 4x - 5 = 0</u>

You could solve that by factoring it, or use the quadratic equation.

Factored, it says that    (x + 1) (x - 5) = 0

From which       <em>x = -1</em>
             and      <em>x = +5</em>

We only want the positive results, so our three consecutive integers are

             5,  6,  and  7 .   

To answer the question, the smallest one is    <em><u>5 </u></em>.

<u>Check</u>:

   5 x 6  ? = ?  (7 x 5) - 5

       30  ? = ?  (35) - 5

         30   =   30

             yay !   


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