Question

find jk.
triangle image with right angle at j, side ij = 6.2, angle at k is 57°
write your answer as an integer or as a decimal rounded to the nearest tenth.
jk =
submit

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle \( \triangle IJK \) with \( \angle J = 90^{\circ} \), \( \angle K=57^{\circ} \) and \( IJ = 6.2 \). We want to find the length of \( JK \). We can use the tangent function. In a right - triangle, \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle K \), the opposite side is \( IJ \) and the adjacent side is \( JK \). So \( \tan(57^{\circ})=\frac{IJ}{JK} \), which can be rewritten as \( JK=\frac{IJ}{\tan(57^{\circ})} \).

Step2: Calculate the value

We know that \( IJ = 6.2 \) and \( \tan(57^{\circ})\approx1.539 \). Then \( JK=\frac{6.2}{\tan(57^{\circ})}=\frac{6.2}{1.539}\approx4.0 \) (rounded to the nearest tenth).

Answer:

\( 4.0 \)