The two acute angles of a right triangle are in the ratio 8:1. Find the number of degrees in each acute angle.?

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  • 1 year ago

    They are 80 and 10 degrees. A right angle is 90 degrees and there are 180 degrees in a triangle, so the remaining two angle measures have to add up to 90 degree.

    if the measures of the two acute angles are in the ratio 8:1, then there are 9 parts.

    90/9 is 10, so 8:1 becomes 80:10.

  • David
    Lv 7
    1 year ago

    The angles are 80 and 10 degrees

  • RR
    Lv 7
    1 year ago

    The internal angles of any triangle total 180 degrees.

    In this right angles triangle, one angle has to be 90 degrees, leaving 90 degrees for the total of the unknown angles.

    You need to divide the remaining 90 degrees in a ratio of 8:1.

    With ratios, add them together to find the number of parts:

    8 + 1 = 9 parts

    1 part = 90x 1/9 = 10 degrees

    8 parts = 8 x 10 = 80 degrees.

    ANS. The angles are 80 degrees and 10 degrees.

  • 1 year ago

    The two acute angles of a right triangle are in the ratio 8 : 1.

    The number of degrees in each acute angle:

    80 degrees and 10 degrees

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  • 1 year ago

    80 degrees and 10 degrees

  • Como
    Lv 7
    1 year ago

    --

    9 parts_________90°

    1 part__________10°

    8 parts_________80°

    Acute angles are 10° and 80°

  • 1 year ago

    The sum of the two remaining angles is 90 degrees.

    Add the ratios 8 + 1 = 9

    Divide 90 by 9 . This will give the alue of one ratio.

    Hence 90/9 = 10

    Hence 8 x 10 = 80

    8:1 :: 80:10 are the two remaining angles.

  • TomV
    Lv 7
    1 year ago

    The sum of the angles is 90°. Broken into an 8:1 ratio requires a total of 9 equal parts of which the larger angle contains 8 of those parts and the smaller contains 1. 90° divided into 9 parts places 10° in each part. Hence the two angles would be 8*10 = 80° and 1*10 = 10°.

    Ans: 80° and 10°

  • DWRead
    Lv 7
    1 year ago

    8x+1x = 90°

    x = 10°

    8x = 80°

  • Robert
    Lv 7
    1 year ago

    The two angles must add up to 90º

    So we have x + 8x = 90, from which

    x = 10

    Thus the angles are 10º and 80º

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