Mathematics

Problem

A tree stands vertically on level ground. From a point

A

on the ground the angle of elevation of the top of the tree is

\theta

and it is observed that

\tan\theta = 0.8

. Use this information to answer the following. a. (i) Calculate

\sec\theta

correct to two decimal places. b. (ii) If the horizontal distance

AB

from point

A

to the foot

B

of the tree is

25\,\text{m}

, find the height of the tree. c. (iii) Determine the length of the line of sight

AC

from point

A

to the top

C

of the tree.