Question

29.3212. IF VS = 12 m, find the length of UT.13. If JH = 21 in, fnd the length of KIG.RH5912785U1114. If FG = 27 yd, find the length of FED.15. If WS = 4.5 mm, find the length of TS.80P12811L7.62Gina Wilson (All Things Algebra), 2015

Answer 1

hello

12.

from a careful observation, one would notice that line VS is the diameter of the circle and ut is the lenght of an arc. however, we have to find the angle UT

`\begin{gathered} vs=180^0 \\ vs=vr+sr \\ vr=127^0 \\ 180=127+sr \\ sr=180-127 \\ sr=53^0 \end{gathered}`

note: vs is equal to 180 degrees because angle on a straight line is equal to 180 degree

`\begin{gathered} ur=180^0 \\ ur=uv+vr \\ 180=uv+127 \\ uv=180-127 \\ uv=53^0 \end{gathered}`

now we can solve for angle UT easily

`\begin{gathered} vs=vu+ut+ts \\ 180=53+ut+90 \\ 180=143^{}+ut \\ ut=180-143 \\ ut=37^0 \end{gathered}`

now we have the value of angle msince we know the value of angle UT, we can use this information to solve for length of the arc of UT

`\begin{gathered} L_(ut)=(\theta)/(360)*2\pi r \\ r=(vs)/(2)=(12)/(2)=6 \\ L_(ut)=(37)/(360)*2*3.142*6 \\ L_(ut)=3.875m \end{gathered}`

from the calculations above, the length of the arc UT is equal to 3.87m