# Trig

posted by .

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 -

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

## Similar Questions

1. ### maths

Choose three options which are true: a) an angle of 150 degrees is equivalent to 2pie/3 radians. b) Cos 0 = cos (0 – pie/2) for al values of 0. c) Sin 0 = cos (0 – pie/2) for all values of 0. d) If triangle ABC has a right angle …
2. ### maths

Choose three options which are true: a) an angle of 150 degrees is equivalent to 2pie/3 radians. b) Cos 0 = cos (0 – pie/2) for al values of 0. c) Sin 0 = cos (0 – pie/2) for all values of 0. d) If triangle ABC has a right angle …
3. ### geometry

5. The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. (a) Find the area of triangle PQR. (b) Find the length of the projection of segment PQ onto segment PR. (c) Find the …
4. ### Trig

The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. (a) Find the area of triangle PQR. (b) Find the length of the projection of segment PQ onto segment PR. (c) Find the length …
5. ### math pls

The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. (d) Find the sizes of the other two angles of triangle PQR. (e) Find the length of the median drawn to side PQ. (f) Find …
6. ### geometry/math pls help

The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P. (1) Find the sizes of the other two angles of triangle PQR. (2) Find the length of the median drawn to side PQ. (3) Find …
7. ### Math

If triangle PQR is 14.5 then PQR=71, QPR =57 find the lengths of the sides PR and PQ
8. ### Math

In obtuse triangle PQR, P=51 degrees, p= 10cm, and the longest side, q=12cm.Draw the triangle and solve for Q to the nearest degree. I did, 10/sin 51=12/sin Q 10(sin Q)/10=12(sin 51)/10 Q= 2nd function sin 0.9325751 Q=68 degrees Q=180-68 …
9. ### Maths

In triangle PQR,angle p=90degree if PQ=√3 and QR=2,then find the value of sinQ ,cosQ,tanR,SINR