In triangle PQR, <R=90 degrees, <Q=10 degrees and RQ=16 cm. Find PR.

sin 10 = PR/16

PR = 16 sin 10

To find the length of PR in triangle PQR, we can use the trigonometric ratio known as the tangent.

Since we are given that angle Q is 10 degrees and angle R is 90 degrees, we can find angle P using the fact that the sum of angles in a triangle is 180 degrees.

Angle P = 180 degrees - Angle Q - Angle R
Angle P = 180 degrees - 10 degrees - 90 degrees
Angle P = 80 degrees

Now, let's use the tangent function to find the length of PR. The tangent of an angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Tangent of angle P = Opposite / Adjacent

In this case, the side opposite angle P is PR, and the side adjacent to angle P is RQ.

Tangent of angle P = PR / RQ

Since we know the values of angle P and RQ, we can substitute them into the equation and solve for PR.

Tangent of 80 degrees = PR / 16 cm

To calculate the tangent of 80 degrees, you can use a scientific calculator or an online trigonometric calculator. The tangent of 80 degrees is approximately 5.6713.

5.6713 = PR / 16 cm

Now, we can solve for PR by cross-multiplying:

PR = 5.6713 * 16 cm
PR ≈ 90.74 cm

Therefore, the length of PR in triangle PQR is approximately 90.74 cm.