Question

find ij.
write your answer as an integer or as a decimal rounded to the nearest tenth.
ij = \boxed{}

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( \triangle HIJ \), \( \angle H = 56^\circ \), \( IH = 4 \) (adjacent side to \( \angle H \)), and \( IJ \) is the opposite side to \( \angle H \). We use the tangent function: \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). So, \( \tan(56^\circ)=\frac{IJ}{IH} \).

Step2: Substitute values and solve

Substitute \( IH = 4 \) and \( \theta = 56^\circ \) into the formula: \( \tan(56^\circ)=\frac{IJ}{4} \). Then, \( IJ = 4\times\tan(56^\circ) \). Calculate \( \tan(56^\circ)\approx1.4826 \), so \( IJ\approx4\times1.4826 = 5.9304 \). Rounding to the nearest tenth gives \( IJ\approx5.9 \).

Answer:

\( 5.9 \)