trig question about a right triangle!?

The hypotenuse of a right triangle is of length 28 and one of the sides of length 11.

What is the measure of either of the acute angles in degrees?

(answer has to be to the nearest tenth)

2 Answers

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  • 9 years ago
    Favorite Answer

    Draw the hypotenuse as a diagonal line from the left and down toward the right and up. Draw one of the other sides horizontally from where the hypotenuse begins left and down, towards the right (as I said, horizontally). Make the third line vertical from the end of the second line up to the end of the hypotenuse. With the information given, the side of length 11 can be either the horizontal side or the vertical side. You will get the same acute angles but in switched positions. Let's say that the horizontal side is 11 and "x" is the angle formed by this side and the hypotenuse.

    Then:

    cos(x) = adjacent side / hypotenuse

    cos(x) = 11 / 28 = 0.39285714285714285714285714285714

    x = 66.9 degrees

    That's one of the acute angles. You can find the other acute angle by realizing that all three angles of a triangle add up to 180 degrees, so if we call the other acute angle "y", then:

    x + y + 90 = 180 -----> y = 90 - x = 90 - 66.9 = 23.1 degrees

    So the measure of the acute angles is 66.9 degrees and 23.1 degrees.

    You can prove this by using the Pythagoras Theorem to find the length of the other side:

    h^2 = a^2 + b^2 -----> b^2 = h^2 - a^2 ----->

    b = sq rt (h^2 - a^2) = sq rt (28^2 - 11^2) = sq rt (784 - 121) = 25.75 = length of other side.

    Then:

    sin(x) = opposite side / hypotenuse = 25.75 / 28 = 0.91959951354169519753005684209598

    x = 66.9 degrees (the same answer as before, which proves the answer).

    I hope this helps...

  • LGN
    Lv 5
    9 years ago

    The problem gives the length of "one of the sides" but does not tell if it is the opposite side or the adjacent side. This is not too significant, though, since the question asks for either acute angle. Simply take either the arcsin (sin^-1) or arccos (cos^-1) of the fraction 11/28 (side/hypotenuse) as these values are the measures of the two acute angles.

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