Question

In ASTU, U = 900 cm,

Answer 1

We shall begin by drawing a sketch of the triangle STU as shown below;

As shown in the triangle above, Angle U and side length u is given. Angle S is calculated as follows;

`\begin{gathered} S+T+U=180(\text{angles in a triangle sum up to 180)} \\ S+49+14=180 \\ S=180-49-14 \\ S=117 \\ \text{Having derived angle S, we shall apply the law of sines as follows;} \\ (a)/(\sin a)=(b)/(\sin b) \\ \text{Substitute for the known values, which are U, S, u and s} \\ (u)/(\sin U)=(s)/(\sin S) \\ (900)/(\sin14)=(s)/(\sin 117) \\ (900*\sin 117)/(\sin 14)=s \\ (900*0.891)/(0.2419\ldots)=s \\ (801.9)/(0.2419)=s \\ 3315.0062=s \\ s\approx3315 \end{gathered}`

Therefore, the length of s is 3,315 cm