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The shorter leg of a 30 degree - 60 degree - 90 degree triangle is 10. What are the lengths of the longer leg and the hypotenuse, to the nearest tenth.

I do not understand these triangles can anyone help??

  • Geometry -

    A 30-60-90 triangle is a right triangle because of the 90 degree angle. The side sith length 10 will be across from the 10 degree angle.

    I don't know if you have studied trigonometry and the trig functions like sin, cos and tan. The "law of sines" would tell you that
    10/sin 30 = b/sin 60 = c/sin 90 = c
    where sin 30 = 1/2 and c is the hypotenuse.
    Thus c = 10/(1/2) = 20 and
    b^2 = c^2 - a^2 = 300
    b = 17.3

    Without using trig, you can use the fact that a 30-60-90 trianle is one-half of an equilateral triangle that is split in two by bisecting one of its 60 degree angles. The short side of one of the pair of triangles thus formed must therefore have a length of half the longest side. The middle side (b) length can be computed with the Pythagorean theorem.

  • Geometry -

    Ok I have not done any trig, but I think I kind of understand what you mean.. thank you.

  • Geometry -

    a right triangle has legs of 24 units and 18 units. the lenght of the hypotenuse is?

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