Question

Right triangle WXY is similar to triangle DEF. The following are measurements in right triangle DEF:What is the value of cos W?A.$\frac{7}{8}$B.$\frac{8}{7}$C.$\frac{ \sqrt{113} }{7}$D.$\frac{7}{ \sqrt{113} }$

Answer 1

Draw a diagram including both triangles to visualize the situation:

Since the angles W and D are corresponding angles through the similarity statement, then:

$\cos (W)=\cos (D)$

The cosine of the angle D equals the ratio of the side adjacent to D to the hypotenuse. The hypotenuse of the triangle DEF has a measure of √113, while the side adjacent to D is DF and has a measure of 7. Then:

$\cos (D)=\frac{7}{\sqrt[]{113}}$

Therefore:

$\cos (W)=\frac{7}{\sqrt[]{113}}$