15.2.3 Trigonometry, PT3 Focus Practice

Question 10:
A technician needs to climb a ladder to repair a street lamp as shown in Diagram below.
(a) What is the length, in m, of the ladder?
(b) Find the height, in m, of the lamp post.

Solution:


(a)
$\begin{array}{l}\text{cos}{70}^o=\frac{1}{h}\\ h=\frac{1}{\text{cos}{70}^o}\\ h=\frac{1}{0.342}\\ h=2.924\text{ m}\\ \\ \text{Hence, the length of the ladder}\\ =2.924\text{ m}\end{array}$

(b)
$\begin{array}{l}\text{tan}{70}^o=\frac{T}{1}\\ T=\text{tan}{70}^o\times 1\\ =2.747\times 1\\ =2.747\text{ m}\\ \\ \text{The height of the lamp post}\\ =2.747+1.2\\ =3.947\text{ m}\end{array}$