Question

1.Find the perimeter of an isosceles triangle whose base is 40 cm and whose base angle is 70".

Answer 1

Since the triangle is isosceles, the other two sides have equal length. Call the length of each side $x$.

Draw a perpendicular from vertex to the base and recall that this is also a bisector of base. Therefore you get a right triangle with a leg $20$ and one angle $70^{\circ}$. The other side can be obtained by applying cosine ratio :
$\cos(70^{\circ})~=~\frac{20}{x}\implies x = \frac{20}{\cos(70^{\circ})}~\approx~58.48$

Add up the sides to get the perimeter
$40+58.48+58.48~=~156.96$