Question

c. 23 cm
plan of attack:
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solve for x:

Explanation:

Step1: Find the height \( h \)

Use the right - triangle with angle \( 15^{\circ} \) and adjacent side \( 63\) cm.
\( \tan15^{\circ}=\frac{h}{63}\), so \( h = 63\tan15^{\circ}\).
Since \( \tan15^{\circ}=2 - \sqrt{3}\approx0.2679\), then \( h=63\times0.2679 = 16.88\) cm.

Step2: Solve for \( x \)

In the right - triangle with hypotenuse \( 23\) cm and opposite side \( h\).
\( \sin x=\frac{h}{23}\), substitute \( h = 16.88\)
\( \sin x=\frac{16.88}{23}\approx0.7339\)
\( x=\sin^{-1}(0.7339)\approx47.2^{\circ}\)

Answer:

\( x\approx47.2^{\circ}\)