Math Problem? Please help.. multiple choice?

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A building lot in a city is shaped as a 30° -60° -90° triangle. The side opposite the 30° angle measures 41 feet. a. Find the length of the side of the lot opposite the 60° angle. ...show more
Best Answer
a. The side opposite the 60° is 71.0141 feet

b. The hypotenuse is 82 feet

c. sin(30)=0.5000

cos(30)=0.8660

tan(30)=0.5773

I would also like to tell you something about 30,60,90 triangles. The side opposite the 90° angle, the hypotenuse, will always be double that of the side opposite the 30° angle. This is one of the reasons why this type of triangle (30,60,90) is considered a special triangle.
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  • Ursus Particularies answered 2 years ago
    30-60-90 is a triangle that is 1/2 of equilateral triangle
    since latter has EQUAL SIDES, 30-60-90 has sides of 1, 2, and sqrt 3
    with the 1 being the side of the equilateral that was bisected (cut in half), also making one 60 degree angle into 30 degrees. 2 is a hypotenuse, opposite the 90 degree angle, 1 is opposite the 30 degree angle, sqrt 3 is opposite the 60 degree angle -- last gives answer for (a) which is sqrt 3 times 41 ft

    (b) answer is 2 times 41 ft

    (c) answers are:

    sine 30 deg = 1/2 or 41/82 ft thus 0.5000
    cos 30 deg = this also left for you
    tan 30 deg = 1/(sqrt 3) or 41 ft / (sqrt 3 x 41 ft) = you compute this

    Source(s):

    1, sqrt 3 and 2 is ratio of sides that applies to 30-60-90 triangle
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  • Pranil answered 2 years ago
    The side opposite the 30° angle measures 41 feet.
    The side opposite the 30° angle is 1/2 the measure of hypotenuse = 41 feet.
    b) so hypotenuse = 41 × 2 = 82 feet

    a) side opposite to 60° is √3/2 × hypotenuse
    = √3/2 × 82 = 41√3

    so sides are
    41, 41√3 and 82
    sin 30 = 41/82 = 1/2 = 0.5000
    cos 30 = 41√3/82 = √3/2 = 0.8660
    tan 30 = sin 30/cos 30
    = 1/2 ÷ √3/2 = 1/√3 = 0.5774
    ------
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  • Roger answered 2 years ago
    a) 41(tan 60°) 41(√3) = 71.01 feet
    b) the hypotenuse is 2 x41 = 82 feet
    c) sin 30° = 0.5000
    cos 30° = (√3)/2 = 0.8660
    tan 30° = 1/(√3) = 0.5774
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  • CDA answered 2 years ago
    Right-angled triangle with angles 30, 60, 90 degrees.
    I presume you know what sines and cosines are.
    If side opposite the 30 deg is 41 feet the hypotenuse is 82 feet since sin30 = 0.5 exactly.
    The other side is 41sqrt3 feet, since sin60 = 1/2. sqrt3

    From any trig tables you can find sin30, cos30, tan30 yourself, to 4 decimals, 5 decimals or more.
    Or you can use a calculator, or even google.
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