geometry

Each base of an isosceles triangle measures 42 degrees, 30'. The base is 14.6 meters long.
a. Find the length of a leg of the triangle
b. Find the altitude of the triangle
c. What is the area of the triangle?

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  1. make a sketch, marking the angles

    draw the altitude, cutting the base into 2 parts of 7.3 each, and giving you right-angled triangles.

    a) leg of triangle = hypotenuse of the right-angled triangle, call it c
    cos 42.5 = 7.3/c
    c = 7.3/cos 42.5 = ....
    b) altitude --- h
    tan 42.5 = h/7.3
    h = 7.3tan 42.5 = ....

    c) area - (1/2) base x heigh
    = (1/2)(14.6)(h) , the h from b)
    = ....

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