Answer:
sin A = \(\frac{16}{65}\)
Step-by-step explanation:
given
cos A = \(\frac{63}{65}\) = \(\frac{adjacent}{hypotenuse}\)
63 and 65 are the sides of a right triangle
with 63 being the adjacent side to ∠ A
and 65 the hypotenuse
To find the opposite side use Pythagoras' identity
• a² + b² = c² ( c is the hypotenuse and a, b the legs )
let a = opposite side, b = 63 and c = 65 , then
a² + 63² = 65²
a² + 3969 = 4225 ( subtract 3969 from both sides )
a² = 256 ( take square root of both sides )
\(\sqrt{a^2}\) = \(\sqrt{256}\)
a = 16
The opposite side to ∠ A in the right triangle is 16 , then
sin A = \(\frac{opposite}{hypotenuse}\) = \(\frac{16}{65}\)
