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XY = 27
YZ = 36
XZ = 42
The side lengths of triangle XYZ are given. Triangle XYZ is similar to triangle PQR, where Y corresponds to Q and Z corresponds to R. What is the value of \(\tan(R)\)?
In triangle \(MNP\), angle \(N\) is a right angle. If \(\sin(P)=\frac5{13}\), what is the value of \(\cos(M)\)? Please provide your answer as a fraction.
Triangle ABC is similar to triangle DEF, where angle A corresponds to angle D and angles B and E are right angles. If \(\tan(A)=\frac{15}{8}\) what is the length of side DF?
In right triangle ABC, the sum of the measures of angle A and angle B is 90 degrees. The value of \(\cos(A)=\frac{\sqrt3}2\). What is the value of \(\cos(C)\)?