Question

solve for x. round to the nearest tenth of a degree, if necessary.
(image of a right triangle hij with right angle at i, hi = 2.8, ij = 4.2, angle at h is x°)

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( HIJ \), we have opposite side to \( x \) as \( IJ = 4.2 \) and adjacent side as \( HI = 2.8 \). So we use tangent function: \( \tan(x)=\frac{\text{opposite}}{\text{adjacent}}=\frac{IJ}{HI}=\frac{4.2}{2.8} \)

Step2: Calculate \( \tan(x) \)

\( \tan(x)=\frac{4.2}{2.8} = 1.5 \)

Step3: Find \( x \) using arctangent

\( x=\arctan(1.5) \). Using calculator, \( x\approx 56.3^\circ \) (rounded to nearest tenth)

Answer:

\( 56.3^\circ \)