What's the value of cos D?

Question

In triangle ABC, the measure of angle B is 90 degrees, BC=80 and AC=100. Triangle DEF is similar to ABC where vertices D, E, and F correspond with vertices A, B, C. The scale factor of DEF to ABC is 1/10. What's the value of cos D?

Answer 1

First, draw your original triangle based on the description with the labels.  Since angle B is 90 degrees, your triangles will be right triangles.  Then use scale factor 1/10 to draw your similar triangle.  Make sure both triangles are labeled correctly and correspondingly.

 

This means that AB and BC are the legs, and AC is the hypotenuse of the original triangle. 

DE and EF are the legs, and DF is the hypotenuse of the similar triangle.

 

There, I gave you the correct labeling and orientation of the triangle's vertices.  You know the two sides of the original triangle.   Use the Pythagorean to get the missing side of the original triangle.   Now all you have to do use the scale factor to get all the sides of the similar triangle using proportions.  Then, use the law of sines or law of cosines to find the missing angles.  Since you want to find the value of cosD, I would try to find angle A.  Remember that similar triangles have congruent corresponding angles.

Answer 2

In similar triangles the corresponding angles are equal.

cos D = cos A

cos A = AB / 100

Use Pythagoras to determine AB.