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The lengths QR, RP, and PQ in triangle PQR are often denoted p, q, and r, respectively.
What do the formulas 1/2 pq sinR and 1/2 qr sin P mean? After you justify the
equation 1/2 pq sinR = 1/2 qr sin P, simplify it to a familiar form.

  • Trig -

    The formulas represent the area of the triangle

    Did you want an actual proof of the formula?

    Hint: draw a perpendicular from P to QR, call it h
    take sinR, then find the area by (1/2)base*height.

  • Trig -

    How do I actually proof the formula?

  • Trig -

    ok, follow my steps above

    you now have a right-angled triangle with a height of h
    sin R = h/PR = h/q
    h = qsin R

    Isn't the area of the triangle (1/2)(base)h
    = (1/2)QRh
    = (1/2)p(qsin R)
    = (1/2)pq sin R as requested.

    dropping perpendiculars from R and Q you can prove in the same way that

    area = (1/2)rq sinP and (1/2)rpsinQ

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