Question

Find the value of x.
Round to the nearest tenth.
34
A
B
26°
x = [? ]°
X
C
15

Answer 1

Answer: 83.5

Step-by-step explanation:

$\frac{\sin x}{34}=\frac{\sin 26^{\circ}}{15} \\\\\sin x=\frac{34 \sin 26^{\circ}}{15}\\\\x=sin^{-1} \left(\frac{34 \sin 26^{\circ}}{15} \right) \approx \boxed{83.5}$

Answer 2

Answer:

  x ≈ 83.5° or 96.5°  (two possible values)

Step-by-step explanation:

The relationship between side lengths of a triangle and their opposite angles is given by the Law of Sines: side lengths are proportional to the sines of their opposite angles.

__

In this problem, the Law of Sines tells us ...

  sin(A)/BC = sin(C)/AB

  sin(C) = sin(A)·AB/BC

Using x for angle C, solving for x, and using the inverse sine function, we find ...

  x = arcsin(sin(26°)·34/15) ≈ arcsin(0.993641)

The arcsine function returns a value in the range 0–90°, but the supplemental angle in the rangle 90°–180° can have the identical sine value.

  x ≈ 83.5° or 96.5°

_____

Additional comment

For the graph in the attachment, we have set the angle mode to degrees. The solutions to f(x)=0 are solutions to the problem: 83.5° and 96.5°.

The triangle in the figure appears to be an acute triangle. The value of x for an acute triangle would be 83.5°. Often, we cannot take these figures at face value.