Question

14. Geology To measure the height of a rock formation, a surveyor places her transit
100 m from its base and focuses the transit on the top of the formation. The angle of
elevation is 67. The transit is 1.5 m above the ground. What is the height of the rock!
formation? Round to the nearest meter.

Answer 1

Answer:

237.09m

Step-by-step explanation:

Let's use the tan rule to find the length of the adjacent side.

Tan rule is given as

$Tan \theta=\frac{Opposite \ side}{Adjacent \ side}$

$\theta$=67° , and Adjacent length is given as 100m.

We therefore need to find the length of the adjacent side.

$Tan\theta=\frac{X}{100}\\Tan 67\textdegree=\frac{X}{100}\\X=Tan \ 67\textdegree \times 100\\X=235.58m$

To find height of the rock, we add X value to transit height=$235.58+1.5=237.09m$

*See pic for graphic illustration