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 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?
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Answer 1

Answer:

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