Respuesta :
Answer:
[tex]a\approx 31[/tex]
[tex]b\approx 72[/tex]
Step-by-step explanation:
Please find the attachment.
We have been given that in triangle ABC, A=25, C=55 and AB=60. We are asked to find the approximate measures of the remaining side lengths of the triangle.
We will use Law of Sines to solve for side lengths of given triangle.
[tex]\frac{\text{sin}(A)}{a}=\frac{\text{sin}(B)}{b}=\frac{\text{sin}(C)}{c}[/tex], where a, b and c are opposite sides corresponding to angles A, b and C respectively.
Upon substituting our given values, we will get:
[tex]\frac{\text{sin}(25)}{a}=\frac{\text{sin}(55)}{60}[/tex]
[tex]a=\frac{60\text{sin}(25)}{\text{sin}(55)}[/tex]
[tex]a=\frac{60*0.422618261741}{0.819152044289}[/tex]
[tex]a=\frac{25.35709570446}{0.819152044289}[/tex]
[tex]a=30.9552980807967304[/tex]
[tex]a\approx 31[/tex]
Therefore, the measure of side 'a' is approximately 31 units.
We can find measure of angle B using angle sum property as:
[tex]m\angle A+m\angle B+m\angle C=180[/tex]
[tex]25+m\angle B+55=180[/tex]
[tex]m\angle B+80=180[/tex]
[tex]m\angle B=100[/tex]
[tex]\frac{\text{sin}(100)}{b}=\frac{\text{sin}(55)}{60}[/tex]
[tex]b=\frac{60\text{sin}(100)}{\text{sin}(55)}[/tex]
[tex]b=\frac{60*0.984807753012}{0.819152044289}[/tex]
[tex]b=\frac{59.08846518072}{0.819152044289}[/tex]
[tex]b=72.1336967815383509[/tex]
[tex]b\approx 72[/tex]
Therefore, the measure of side 'b' is approximately 72 units.
