who is acquainted eith trigonometry?

Question

How does one solve this?..The diagonals of a rectangle each measure 22 and intersect at an angle whose measures is 110 dgrees. Find to the nearest integer the length and width of the triangle?

Answer 1

I assume you mean the length and the width of the rectangle.

Sketch it. The diagonals of the rectangle are the hypotenuses of two congruent right triangles, each comprising half of the rectangle. The length and width of the rectangle will be the legs of that triangle. If the diagonals intersect at 110 degrees, then they also intersect at 70 degrees - whoever wrote the question is being less than precise. Because the diagonals of a rectangle bisect each other, that 110 degree angle is the apex angle of an isosoles triangle, meaning that the base angles are 35 degrees. That will be one of the acute angles in the right triangle we mentioned above. From the right triangle relations,

sin 35 = width/22

cos 35 = length/22

and it's calculator time.

When you have problems like this, it is always a good idea to make a sketch of the situation to start. As good an idea as it is, an amazing number of students never bother with it.