Question

math 2201 september 2025 2)the worlds tallest free - standing totem pole is located in beacon hill park in victoria, british columbia. it was carved from a single cedar log by noted carver chief mungo martin of the kwakiutl (kwakwakawakw), with a team that included his son david and henry hunt. it was erected in 1956. while visiting the park, manuel wanted to determine the height of the totem pole, so he drew a sketch and made some measurements: 3)brendan and diana plan to climb the cliff at dry island buffalo jump, alberta. they need to know the height of the climb before they start. brendan stands at point b, as shown in the diagram. he uses a clinometer to determine /abc, the angle of elevation to the top of the cliff. then he estimates /cbd, the angle between the base of the cliff, himself, and diana, who is standing at point d. diana estimates /cdb, the angle between the base of the cliff, herself, and brendan. determine the height of the cliff to the nearest metre.

Explanation:

Step1: Find length of BC in triangle BCD

In $\triangle BCD$, using the sine - rule $\frac{BC}{\sin\angle BDC}=\frac{BD}{\sin\angle BCD}$. First, find $\angle BCD = 180^{\circ}-(50^{\circ}+60^{\circ}) = 70^{\circ}$, and $BD = 60$ m. So, $BC=\frac{BD\times\sin\angle BDC}{\sin\angle BCD}=\frac{60\times\sin50^{\circ}}{\sin70^{\circ}}$.
$\sin50^{\circ}\approx0.766$, $\sin70^{\circ}\approx0.9397$, then $BC=\frac{60\times0.766}{0.9397}\approx48.7$ m.

Step2: Find height of cliff AC in triangle ABC

In right - triangle $ABC$, $\tan\angle ABC=\frac{AC}{BC}$. Given $\angle ABC = 76^{\circ}$, and we found $BC\approx48.7$ m. So, $AC = BC\times\tan\angle ABC$.
$\tan76^{\circ}\approx4.0108$, then $AC\approx48.7\times4.0108\approx195$ m.

Answer:

The height of the cliff is approximately 195 m.