An isosceles triangle has a vertex angle measuring 45°. The two equal sides have length Q inches. What is the length of the base (in inches)?

Question

I need to find the lenth of the base of a triangle isosceles, but they only give me the measure of the vertex and they told me that the two equal sides are equal to q

Answer 1

We can only find the length of the base in terms of q. If we bisect the vertex we have two right triangles and the base is bisected. If the base has length b, then we have two sides of each right triangle: ½b and q. And we have an angle of 45/2=22.5°. Using trigonometry, ½b/q=sin22.5°=0.3827. Therefore b=0.7654q inches.