Question

what is the approximate value of ( y - x )?
( 4.9^circ )
( 6.2^circ )
( 11.1^circ )
( 17.2^circ )
(image shows a right triangle lmn with right angle at l, ln = 19.1 in, lm = 14.1 in, angle at n is ( x ), angle at m is ( y ))

Explanation:

Step1: Find angle \( y \)

In right triangle \( LMN \), \( \tan(y)=\frac{\text{opposite}}{\text{adjacent}}=\frac{LN}{LM}=\frac{19.1}{14.1} \)
\( \tan(y)=\frac{19.1}{14.1}\approx1.3546 \)
\( y = \arctan(1.3546)\approx53.5^\circ \)

Step2: Find angle \( x \)

Since the triangle is right - angled at \( L \), \( x + y=90^\circ \), so \( x = 90^\circ - y \)
\( x=90^\circ - 53.5^\circ = 36.5^\circ \)

Step3: Calculate \( y - x \)

\( y - x=53.5^\circ-36.5^\circ = 17.0^\circ\approx17.2^\circ \) (due to rounding differences in the calculation of \( \arctan \))

Answer:

\( 17.2^\circ \)