In the figure above, triangle ABC is similar to triangle DEF . What is the value of cos(E) ?

Options

A. `12/5`
B. `12/13`
C. `5/12`
D. `5/13`

Answer

B

Explanation

Since figures are drawn to scale unless otherwise stated and triangle ABC is similar to triangle DEF, it follows that the measure of angle B is equal to the measure of angle E. Furthermore, it follows that side AB corresponds to side DE and that side BC corresponds to side EF. For similar triangles, corresponding sides are proportional, so `(AB)/(BC)=(DE)/(EF)`. In right triangle DEF, the cosine of angle E, or cos(E ), is equal to the length of the side adjacent to angle E divided by the length of the hypotenuse in triangle DEF. Therefore `cos(E)=(DE)/(EF)`, which is equivalent to `(AB)/(BC)`. Therefore , cos(E)=`12/13` .
Choice A is incorrect. This value represents the tangent of angle F, or tan(F ), which is defined as the length of the side opposite angle F divided by the length of the side adjacent to angle F. Choice C is incorrect. This value represents the tangent of angle E, or tan(E ), which is defined as the length of the side opposite angle E divided by the length of the side adjacent to angle E. Choice D is incorrect. This value represents the sine of angle E, or sin(E ), which is defined as the length of the side opposite angle E divided by the length of the hypotenuse.