Question

In triangle ABC, the measure of C is 90°,
AC=24, and BC=10. What is the value of sin
A?

Answer 1

Sin A = 0.38462

Explanation:

From the trigonometric function,

Sin A =
`(Opposite)/(Hypotenuse)` ................... 1

So that, applying the Pythagoras theorem to determine the value of hypotenuse,

`/Hyp/^(2)` =
`/Opp/^(2)` +
`/Adj/^(2)`

=
`24^(2)` +
`10^(2)`

= 576 + 100

`/Hyp/^(2)` = 676

Hyp =
`√(676)`

= 26

The hypotenuse of the triangle is 26.

Thus, from equation 1;

Sin A =
`(10)/(26)`

Sin A = 0.38462