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mojhsa [17]
2 years ago
3

Given △QRS ~ △XYZ, what is the value of tan(Q)?

Mathematics
2 answers:
asambeis [7]2 years ago
6 0

Answer:

tan(Q) = 0.75

Step-by-step explanation:

It is given that triangle XYZ and ΔQRS qre similar.

Sides XY = 15, XZ = 12 and YZ = 9.

We have to calculate tan (Q).

SInce ΔQRS ~ ΔXYZ

Therefore ratio of the corresponding sides of the triangles will be equal.

QR/XY = RS/YZ = QS/XZ

QR/15 = RS/9 = QS/12

Since tan (Q) = RS/QS

and RS/9 = QS/12

RS/QS = 9/12 = 3/4

tan(Q) = 3/4 = 0.75

Answer is tan(Q) = 0.75

Strike441 [17]2 years ago
5 0

Answer:

\text{tan}(Q)=\frac{3}{4}

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.

\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}

\text{tan}(Q)=\frac{RS}{QS}

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

Substituting values:

\text{tan}(Q)=\frac{9}{12}

Simply the fraction:

\text{tan}(Q)=\frac{3*3}{3*4}

\text{tan}(Q)=\frac{3}{4}

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

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