Homework Help: Trig

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

Answer this Question

Related Questions

Trig - The lengths of segments PQ and PR are 8 inches and 5 inches, respectively...
geometry - 5. The lengths of segments PQ and PR are 8 inches and 5 inches, ...
maths - In a triangle ABC, AB = 2 cm, BC = 3 cm and AC = 4 cm. Choose the two ...
Algebra - In triangle PQR shown, point S (not shown)is on QR between Q and R. ...
trig - Triangle PQR is congruent to P'Q'R. If PQ= x+y, P'Q'+10, ...
geometry - The lengths of segments PQ and PR are 8 inches and 5 inches, ...
geometry - The lengths of segments PQ and PR are 8 inches and 5 inches, ...
math pls - The lengths of segments PQ and PR are 8 inches and 5 inches, ...
geometry/math pls help - The lengths of segments PQ and PR are 8 inches and 5 ...
geometry - if in triangle JKL, JK= 9, KL = 11, and JL=12, and in triangle PQR, ...

For Further Reading

First Name:
School Subject:
Answer: