Ask Question
21 March, 10:05

Triangle J L K. Side L K is 4 meters and K J is 3 meters. Angle L is 48 degrees and angle K is 90 degrees. Triangle M O N. Side M O is 1.5 meters, O N is 2 meters, and N M is 2.5 meters. Angle O is 90 degrees.

Use properties of similar triangles to answer the questions.

What is the measure of angle J?

Which side of △MNO corresponds to JK?

What is the ratio of the larger triangle to the smaller triangle?

+3
Answers (1)
  1. 21 March, 12:16
    0
    Step-by-step explanation:

    Triangles are similar if they have the same shape, but not necessarily the same size.

    in this case we have

    JK/MO = KL/ON = JL/MN

    A) Use properties of similar triangles.

    The measurement of angle J can be derived from triangle MNO.

    Corresponding angle are congruent.

    Angle J in triangle JKL correspond with angle M in triangle MNO.

    Therefore:

    Tangent M = opp/adj

    tanM = 2/1.5

    tanM = 1.3

    M = tan-¹ 1.3

    M = 52.43

    J = M = 52.43°

    B) MO in △MNO corresponds to JK in △JKL

    C) JK/MO = KL/ON = JL/MN

    find JL using Pythagoras theorem

    JL² = KL² + JK²

    JL² = 4²+3²

    JL = √ (16+8)

    JL = 5

    JK/MO = KL/ON = JL/MN

    = 3/1.5 = 4/2 = 5/2.5 = 2/1

    Therefore the ratio of larger triangle to small triangle is 2:1
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Triangle J L K. Side L K is 4 meters and K J is 3 meters. Angle L is 48 degrees and angle K is 90 degrees. Triangle M O N. Side M O is 1.5 ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers