As it's Given one two angles of triangle is 60°
let other angle be d
2 × 60° + d = 180°
d = 180° - 120°
d = 60°
All angles of triangle are equal
I.e 60°
.°. Triangle is equilateral and all sides are also equal.
[tex] \tt \: s = \dfrac{a + b + c}{2} [/tex]
So:-
[tex] \tt \: s = \dfrac{3 \times 30}{2} [/tex]
[tex] \\ \\ [/tex]
[tex] \tt \: s = \dfrac{90}{2} [/tex]
[tex] \\ \\ [/tex]
[tex] \tt \: s = 45[/tex]
Now Let's find Area:-
[tex] \\ \\ [/tex]
[tex] \tt area = \sqrt{s(s - a)(s - b)(s - c)} [/tex]
[tex] \\ \\ [/tex]
[tex] \to \tt area = \sqrt{45(45 - 30)(45 - 30)(45 - 30)} \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \to \tt area = \sqrt{45 \times 15 \times 15 \times 15} \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \to \tt area =15 \sqrt{9 \times 5 \times 15} \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \to \tt area =15 \sqrt{3 \times 3 \times 5 \times 15} \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \to \tt area =15 \times 3 \sqrt{ 5 \times 15} \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \to \tt area =15 \times 3 \times 5 \sqrt{3} \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \to \tt area =15 \times 3 \times 5 \times 1.732[/tex]
[tex] \\ \\ [/tex]
[tex] \to \tt area =389.7[/tex]
