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.
`(7)/(8)`B.
`(8)/(7)`C.
`( √(113) )/(7)`D.
`(7)/( √(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}}`