Trigonometry Problem

Question

A square with an area of 16cm2 is surrounded by four congruent triangles,forming a larger square with an area of 90cm2.If each of the triangles has an angle of theta on the vertices of the larger square,find the value of tanTheta.

Answer 1

Since we can't draw a figure, making a larger square of area 90 cm², then each edge of the added on triangle is 4 by (3/2)√10. This make a larger square having each side of [2(3/2)√10]² = 90 cm².

Each of these triangles has an angle of θ at the top of the isosceles triangle with sides of (3/2), (3/2), 4.

And θ has an angle of 90° which forms the 4 corners of the larger square.

And each of the side angles of these isosceles triangles the is 45°. And therefore the

Tan(45°) = 1

I wish we could draw solutions and present them appropriately.