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25 January, 18:54

The base is a 30-60-90 triangle with a hypotenuse of 10 m. the height of the prism is 15 m. find the volume to the nearest tenth.

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  1. 25 January, 21:00
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    First we look for the area of the base of the prism:

    A = (1/2) * (b) * (h)

    Where,

    b: base of the triangle

    h: height of the triangle

    For the base we have:

    b = 10 * sine (30)

    b = 5

    For the height we have:

    h = 10 * sine (60)

    h = 8.7

    Substituting we have:

    A = (1/2) * (5) * (8.7)

    A = 21.75

    The prism volume will be:

    V = A * H

    Where,

    H: prism height

    V = (21.75) * (15)

    V = 326.25

    Round to the nearest tenth:

    V = 326.3 m ^ 3

    Answer:

    the volume is:

    V = 326.3 m ^ 3
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