Chapter 9.9, Problem 17PSB

To determine

To prove:The congruency of $\sin \angle E\&\cos \angle A$

Explanation of Solution

Given information:The following information has been given

EQU is an equilateral triangle

RAT is right triangle at angle T

  $RA=2$

  $RT=1$

Formula used:We know that for any two complementary angles, sine of one will be equal to cosine of the other.

Proof:We see in the triangle RAT, that

  $\cos \angle A=\frac{RT}{RA}=\frac{1}{2}$

Now, in triangle EQU, as all the angles are ${60}^0$ , we can say that

  $\sin \angle E=\sin \angle {60}^0=\frac{1}{2}$

Hence, we can see from the results that

  $\sin \angle E=\cos \angle A$