Question

in this figure, sin(a) = 2/3. what is the value of cos(b)?

Explanation:

Step1: Use the property of complementary angles

In a right - angled triangle, if \(a + b=90^{\circ}\), then \(\cos(b)=\sin(a)\) (cofunction identity: \(\cos(\theta)=\sin(90^{\circ}-\theta)\)).

Step2: Substitute the given value of \(\sin(a)\)

Given that \(\sin(a)=\frac{2}{3}\), since \(\cos(b)=\sin(a)\) (because \(a + b = 90^{\circ}\) in the right - angled quadrilateral (the two non - right angles of a right - angled triangle formed by the diagonal of the rectangle are complementary)).

Answer:

\(\frac{2}{3}\)