Triangle Lengths

Question

In the triangle PQR, angle Q is the Right angle. Sides p and r both measure 10 meters. What is tan P?

Answer 1

We have an isosceles right triangle PQR with the right angle at Q and QR = PQ = 10 meters.

For your information side r or PQ is the side opposite angle R and side p or QR is the side opposite angle P

All 3 angles of a triangle have a sum of 180 degrees. Since both angle P and angle R are equal (definition of an isosceles triangle) and therefore 45 degrees each since their sum must be 90 degrees.

This means that QR (opposite side of angle P) = QR (adjacent side of angle P).

The tan of angle P is the ratio of the side opposite angle P over the side adjacent to angle P.

Both of these sides are 10 meters.

So, tan of angle P = 10/10 or 1

Answer 2

isosceles triangle? tan 45 deg = 1