Chapter 11, Problem 9CUR

To determine

To state: The statement is true / false.

Answer to Problem 9CUR

True

Explanation of Solution

Given:

Right angled triangle.

Formula used:

  1. $\cos \theta =\frac{Base}{Hypotenuse}$

  2. $\sin \theta =\frac{Perpendicular}{Hypotenuse}$

Kindly refer to the right angled triangle as shown in the figure below:

  

$\Delta DEF$ has a right angle at point $E$ .

Let $\angle F=x°$

By sum of angles of a triangle property:

  $\angle D=(90-x)°$

The two acute angles here are $\angle D,\angle F$ .

Taking sine of $\angle D$ .

  $\sin x=\frac{DE}{DF}$

Taking cosine of $\angle F$ :

  $\cos (90-x)=\frac{DE}{DF}$

Therefore, the given statement is true.