Hence, The distance of S from A is 45.2km and distance of S from B is 33.6km
An illustrative diagram for the scenario is shown in the attachment below
From the diagram,
The distance of S from A is given by /AS/ = b
Consider Δ ASB
/AB/ = 25km, <A = 47° and <B = 100° <S = 33°
To determine /AS/
From Sine rule, we can write that
[tex]\frac{/AS/}{sinB}= \frac{/AB/}{sinS}[/tex]
∴ [tex]\frac{/AS/}{sin100^{o} }= \frac{25}{sin33^{o} }[/tex]
[tex]/AS/= \frac{25 \times sin100^{o}}{sin33^{o} }[/tex]
[tex]/AS/= \frac{25 \times 0.9848}{0.5446}[/tex]
[tex]/AS/= 45.2075[/tex] km
/AS/ ≅ 45.2 km
The distance of S from A is 45.2km
For the distance of S from B
In the triangle, the distance between S and B is given by /SB/ = a
From Sine rule, we can also write that
[tex]\frac{/SB/}{sinA}= \frac{/AB/}{sinS}[/tex]
[tex]\frac{/SB/}{sin47^{o} }= \frac{25}{sin33}[/tex]
[tex]/SB/= \frac{25 \times sin47^{o}}{sin33^{o} }[/tex]
[tex]/SB/= \frac{25 \times 0.7314}{0.5446}[/tex]
[tex]/SB/= 33.5751[/tex] km
/SB/ ≅ 33.6 km
The distance of S from B is 33.6km
Hence, the distance of S from A is 45.2km and distance of S from B is 33.6km
Learn more here: https://brainly.com/question/23468484
