Question

Which equation can be used to find the length of AC?

Answer 1

With respect to the given angle of 40°

AC = b, is the opposite side

AB = 10 in is the hypotenuse.

Using the rules of trigonometric ratios,

We know the ratio associating opposite & hypotenuse  is sin.

So we have

$sin\theta= \frac{Opposite}{Hypotenuse}$

Substituting the values we get

$sin 40^{0}  = \frac{b}{10}$

Multiplying both sides by 10 we get

b = 10 sin 40°

So

AC = 10 sin40°

First option is the right answer.

Answer 2

Answer:

(10)sin(40°) = AC

Step-by-step explanation:

From trigonometric definition:

sin(angle) = (opposite side)/hypotenuse

Here the angle is 40°, the opposite side to this angle is segment AC and the hypotenuse is 10 inches length. Replacing this information in the aforementioned definition we get:

sin(40°) = AC/10

Isolating AC:

(10)sin(40°) = AC