Question

In triangle PQR we have angle P is equal to 50 degree angle Q is equal to 60 degree and Angle R is equal to 70 degree three in circles of the triangle touches side QR RP and PQ at point S, T and U respectively. Angle TSU is equal to​

Answer 1

PQR is a RAT with the right angle at R. <P = 30 deg and <Q = 60 deg.

tan P = QR/PR = 1/3^0.5 = 1x/3^0.5x

Now 1x+3^0.5x = p+s = 6, or

(1+3^0.5)x = 6, or

x = 6/(1+3^0.5) = 2.19615242 (i.e. QR), and

3^0.5x =3^0.5*2.19615242 = 3.803847577 (which is the same as 6 - 2.19615242) (i.e. PR)

Now PQ^2 = PR^2 + QR^2 =3.803847577^2 + 2.19615242^2 = 19.29234184, or

PQ = 19.29234184^0.5 = 4.392304844

PQ = 4.392304844