Question

in the following triangle, find length ms. round to the nearest tenth. triangle image with right angles at t and s, segments: jl with jm=6.9, ml=12.9, tl=8.3 ms = blank show calculator

Explanation:

Step1: Identify Similar Triangles

Triangles \( JSM \) and \( JLT \) are similar (by AA similarity, as both are right triangles and share \( \angle J \)). So, the ratios of corresponding sides are equal: \( \frac{JM}{JL} = \frac{MS}{LT} \).

Step2: Calculate \( JL \)

\( JL = JM + ML = 6.9 + 12.9 = 19.8 \).

Step3: Set Up Proportion

Substitute known values: \( \frac{6.9}{19.8} = \frac{MS}{8.3} \).

Step4: Solve for \( MS \)

Cross - multiply: \( MS=\frac{6.9\times8.3}{19.8} \).
Calculate numerator: \( 6.9\times8.3 = 57.27 \).
Then, \( MS=\frac{57.27}{19.8}\approx2.9 \).

Answer:

\( 2.9 \)