Question

A local Outdoors Club has just hiked to the south rim
of a large canyon, when they spot a climber attempting
to scale the taller northern face. Knowing the distance
between the sheer walls of the northern and southern
faces of the canyon is approximately 175m, they
attempt to compute the distance remaining for the
climbers to reach the top of the northern rim. Using
a homemade transit, they sight an angle of depression
of 60c to the bottom of the north face, and angles of
elevation of 30c and 45c to the climbers and top of the
northern rim respectively.
(a) How high is the southern rim of the canyon?
(b) How high is the northern rim?
(c) How much farther until the climber reaches the
top?

Answer 1

Let’s first find the distances h h s, 1 and h2 in the

diagram below, then answer the questions.

tan 60c h

175 = s ; hs = 175 60 tan c = 175 3 m

tan 30c h

175 = 1 ; h1 = 175 30 tan c 3

175 = m

tan 45c h

175 = 2 ; h2 = 175 45 tan c = 175 m

(a) hs = 175 3 m is the height of the south rim.

(b) h h s + 2 = 175 3 175 175 1 3 + = ^ h + m is the

height of the north rim.

(c) h h 175

3

175 2 1 − = − 175 1

3

1 = d n − m is how far

the climbers have to go to the top.