The sine of angle x in right triangle ABC, with sides CD, CB, BD, and BA, is found to be 0.894, established through the principles of trigonometry and triangle similarity.
The correct answer is option C.
The sine of an angle is a fundamental trigonometric function, defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. In the context of a right triangle ABC, the objective is to determine the value of sin x, where angle x is one of the acute angles.
Examining the right triangle ABC, the figure is partitioned into three similar triangles: ΔCDB, ΔBDA, and ΔCBA. The concept of similarity, denoted by the symbol ~, establishes that these triangles share proportional sides.
Considering the similarity between ΔCDB and ΔCBA, the ratio of the side CD to CB is equivalent to the ratio of BD to BA, both measuring 16/17.89. This implies that BD/BA is 0.894.
Given the definition of sine as the ratio of the side opposite the angle (BD) to the hypotenuse (BA), sin x is calculated as 0.894.
In summary, within the specified right triangle, the sine of angle x is 0.894, determined through the principles of trigonometry and the concept of similarity in similar triangles.
Option c is the correct option.
The question probable may be:
BC = 17.89
DC = 16
with reference to the figure sin x=?
a.0.250
b. 0.447
c.0.894
d. 1