Find the height of a tree if the angle of elevation to its topmost part changes from \( 25^{\circ} \) to \( 45^{\circ} \) as the observer moves 10 m closert to the base of the tree.

Question 36, 3.4.7 Part 1 of 3 Suppose that point \( P \) is on a circle with radius \( r \), and ray \( O P \) is rotating with angular speed \( \omega \). Complete parts (a) through (c). \( \mathrm{r}=8 \mathrm{~cm}, \omega=\frac{\pi}{8} \) radian per sec, \( t=3 \mathrm{sec} \)

2. The angles of elevation of the top of a tree from \( P \) and \( Q \) which are 30 m apart are \( 22^{\circ} \) and \( 32^{\circ} \) respectively. Given that the two points are on the same side of the tree and on straight line, determine the height of the tree. ( 4 mks )

Find the exact values of the six trigonometic functions for the following angle. \[ 330^{\circ} \]

\( \tan \theta=-\frac{3}{4} \), given that \( \theta \) is in quadrant IV

As part of her assignment, Devi has to use her clinometer to measure the height of an office tower \( T A \). From a point \( B \), she observes that angle \( T B A=34^{\circ} \). She then walks 25 m away from the office tower to a point \( C \) and observes that angle \( T C A=26^{\circ} \). Find the height of the sfice tover.