Question 23

Explanation

Given a regular square pyramid P.QRST with base edge $3$ cm and lateral edge $3\sqrt{2}$ cm

Consider Triangle TQR

Calculate the length of $TR$ using the Pythagorean theorem on the right triangle at the base

Calculating TO

Since $O$ is the center of the base, $TO$ is half of the diagonal $TR$

Calculating PO

Use the Pythagorean theorem on triangle $PTO$

Calculating Tangent of Angle

The tangent of angle $\alpha$ between line PT and base QRST

Therefore, the tangent of the angle between line PT and base QRST is $\sqrt{3}$