Question

In ARST, the measure of ZT=90°, the measure of ZR=39°, and TR = 55 feet. Find thelength of ST to the nearest tenth of a foot.39°TR55

Answer 1

Apply the sine rule in triangle RST,

`(ST)/(\sin R)=(RS)/(\sin T)=(TR)/(\sin S)`

Substitute the values,

`(ST)/(\sin39)=(RS)/(\sin90)=(55)/(\sin S)`

We know that the sum of all angles of a triangle is 180 degrees,

`\angle R+\angle S+\angle T=180\Rightarrow39+\angle S+90=180\Rightarrow\angle S=51`

Substitute this value,

`(ST)/(\sin39)=(RS)/(\sin90)=(55)/(\sin51)\Rightarrow ST=\sin 39*(55)/(\sin51)\Rightarrow ST\approx44.5`

Thus, the length of side ST is 44.5 feet approximately.