Respuesta :

Answer:

[tex]\text{tan}(Q)=\frac{3}{4}[/tex]

Step-by-step explanation:

We have been given two similar triangles. We are asked to find the value of tan(Q).

Since △QRS ~ △XYZ, so corresponding sides of both triangles will be proportional and corresponding angles are equal.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(Q)=\frac{RS}{QS}[/tex]

We can see that side XZ corresponds to side QS and side YZ corresponds to side RS.

Substituting values:

[tex]\text{tan}(Q)=\frac{9}{12}[/tex]

Simply the fraction:

[tex]\text{tan}(Q)=\frac{3*3}{3*4}[/tex]

[tex]\text{tan}(Q)=\frac{3}{4}[/tex]

Therefore, the value of tan(Q) is [tex]\frac{3}{4}[/tex].

raphealnwobi

The value of tan(Q) in triangle QRS is 3/4.

Similar figures

Two figures are said to be similar to each other if they have the same shape and the ratio of their corresponding sides are proportional. Corresponding angles are equal.

Given that triangle QRS is proportional to triangle XYZ

∠Q = ∠X, ∠S = ∠Z, ∠R = ∠Z

tan(Q) = tan(X) = 9/12

tan(Q) = 3/4

The value of tan(Q) in triangle QRS is 3/4.

Find out more on Similar figures at: https://brainly.com/question/2644832

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