Trig

An isosceles triangle has a height of 12.5 m (measured from the unequal side) and two equal angles that measure 55°. Determine the area of the triangle.

Split in half the triangle is a right triangle, so it's three angles are 90%, 55% and 70%.

I'm still not sure how to find the area.

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  1. If the base is 2x, then

    12.5/x = tan 55°

    The area is just 12.5x

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  2. If you split it in half, the three angles are 90, 55, and 35 for one half. You basically find the base of one half of the triangle, multiply it by 2 (to find the base of the full triangle), multiply that by the height and divide it by 2:

    tan55=12.5/x
    xtan55/tan55=12.5/tan55
    x=8.7526 (Rounded)

    2x=2(8.7526)=17.5052 (Rounded)

    A=bh/2
    A=(17.5052)(12.5)/2
    A=109.4m^2 (Rounded)

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