In triangle PQR. $\angle Q$ is a right angle, QR=24, and PR=26. Triangle YXZ is similar to triangle PQR, where vertices X, Y, and Z correspond to vertices P, Q, and R, respectively, and each side of triangle XYZ is $\frac{1}{2}$ the length of the corresponding side of triangle PQR. What is the value of sin Z?

In triangle ABC, the measure of $\angle B$ is ${90}^{\circ }$, BC = 16, and AC = 20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is $\frac{1}{3}$ the length of the corresponding side of triangle ABC. What is the value of sin F ?

In triangle XYZ (not shown), the measure of $\angle Y$ is ${90}^{\circ },YZ=12,\text{and}XZ=15.$ Triangle HJK is similar to triangle XYZ, where vertices H, J, and K corresponds ot vertices X, Y, and Z, respectively, and each side of triangle HJK is $\frac{1}{5}$ the length of the corresponding side of triangle XYZ. What is the value of tanK?

Triangle PQR is a right tyriangle with the ${90}^{\circ }$ angle at vertex Q. The length of side PQ is 25 and the length of side QR is 60. Triangle STU is similar to trianlge PRQ. The vertices S,T,and U correspond to vertices P, Q, and R, respectively. Each side of triangle STU is $\frac{1}{10}$ the length of the corresponding side of triangle PRQ. What is the value of $\cos \angle U$ ?

The perimeters of two similar triangles are 25cm and 15cm respectively. If one side of first triangle is 9cm, what is the corresponding side of the other triangle?

Triangle PQR has right angle Q. If sin $R=\frac{4}{5}$, what is the value of tan P ?

Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it where sides are $\frac{2}{3}$of the corresponding sides of the first triangle.

The areas of two similar triangles are $36c{m}^2$ and $100c{m}^2$ . If the length of a side of the smaller triangle in 3 cm, find the length of the corresponding side of the larger triangle.

The areas of two similar triangles are $36c{m}^2$ and $100c{m}^2$ . If the length of a side of the smaller triangle in 3 cm, find the length of the corresponding side of the larger triangle.

The areas of two similar triangles are $169c{m}^2$ and $121c{m}^2$ respectively. If the longest side of the larger triangle is 26cm, what is the length of the longest side of the smaller triangle?

P(3, 4), Q(7, -2) and R(-2, -1) are the vertices of triangle PQR. Write down the equation of the median of the triangle through R.