Which equation is correct? (1 point)

Question

triangle ACB, angle C is a right angle, angle B measures g degrees, angle A measures h degrees, segment AC measures x, segment CB measures y, and segment AB measures z

sin g° = z ÷ x

sin g° = x ÷ z

tan g° = z ÷ x

tan g° = x ÷ z

Answer 1

In triangle ACB, where angle C is a right angle, we can use the definitions of the trigonometric functions to determine which equation is correct.

1. We have:

   • \( \sin(g^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} \)
   • \( \tan(g^\circ) = \frac{\text{opposite}}{\text{adjacent}} \)

2. In this triangle:

   • Angle B is \( g \).
   • The side opposite angle B is segment AC (which measures \( x \)).
   • The hypotenuse is segment AB (which measures \( z \)).
   • The side adjacent to angle B is segment CB (which measures \( y \)).

Based on this information:

• The sine of angle B (g) is given by:

  \[ \sin(g^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{AC}{AB} = \frac{x}{z} \]

So the correct equation would be:

\[ \sin(g^\circ) = \frac{x}{z} \]

3. The tangent of angle B (g) is given by:

   \[ \tan(g^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{AC}{CB} = \frac{x}{y} \]

Since we want to find the relationship involving z and x related to tan(g), we express it as:

• Based on trigonometry definitions, since we don't have an equation in terms of y or we can't relate y in terms of x and z directly here.

4. Therefore:

• The correct equation from your provided options is:

None from the selection was appropriately derived from the context for sine or tangent according to the definitions.

However, if we need to determine which of the provided options are mathematically valid from the context of angle \( g^\circ \):

• The correct sine relation is not directly provided.

The selection does not include \( \sin(g^\circ) = \frac{x}{z} \), and the options would not fit directly into \( g^\circ \) context without misinterpretation. So if narrowing down to directly matching tangent:

4. The final verification leads us to conclude: Thus, if further narrowed down to the provided points: Depending on the proportion.

So, if focusing solely on hypotenuse, we'd solve where we equated

None as valid. The required sinusoidal keys lead to adjustments beyond proportions involved.

Therefore, none of the options is strictly correct as laid out for precise relation pairing directly.