Posted by **sarah** on Monday, April 12, 2010 at 7:21pm.

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 -
**Reiny**, Monday, April 12, 2010 at 7:25pm
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 -
**sarah**, Monday, April 12, 2010 at 7:30pm
How do I actually proof the formula?

- Trig -
**Reiny**, Monday, April 12, 2010 at 7:43pm
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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