Question

find tan j and tan k. write each answer as a fraction and as a decimal rounded to four places. right triangle with right angle at l, lk=8, lj=15, jk=17 tan j = \square = \square tan k = \square = \square

Explanation:

Step1: Recall the tangent ratio

In a right triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. For angle \( J \), the opposite side is \( LK = 8 \) and the adjacent side is \( LJ = 15 \). So, \( \tan J=\frac{\text{opposite}}{\text{adjacent}}=\frac{LK}{LJ} \).
\( \tan J = \frac{8}{15} \approx 0.5333 \)

Step2: Find \( \tan K \)

For angle \( K \), the opposite side is \( LJ = 15 \) and the adjacent side is \( LK = 8 \). So, \( \tan K=\frac{\text{opposite}}{\text{adjacent}}=\frac{LJ}{LK} \).
\( \tan K = \frac{15}{8} = 1.875 \)

Answer:

\( \tan J=\frac{8}{15}\approx0.5333 \)
\( \tan K=\frac{15}{8} = 1.875 \)