How do you work out the base of an isosceles triangle with all other sides and angles given?

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I have the sides of the triangle as $2613$ m and $2613$ m for each one. The top angle is $174$ degrees and the bottom angles are $3$ degrees each. How do I work this out? (please give method not just answer)

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In isosceles triangle altitude to the base is also median of the base and bisector of the vertex angle. So draw the altitude and you will get right triangle with hypotenuse $2613$ and angle opposite half of the base equal to $87°$. Thus half of the base is $2613 \cdot \sin 87° \approx 2609.4$.