Question

Find the value of x.

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

Answer 1

Answer: 83.5

Explanation:

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

Answer 2

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

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.

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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°

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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.