Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Relationships in Space: Geometry and Trigonometry in 2D and 3D, Exercise 13: Exercise 11D

A man standing on a cliff looks down with an angle of depression of $40°$ to a boat in the water below the cliff. The cliff is $80$ metre high and the man's eyes are $1.5$ metre above the cliff. How far (in metre) is the boat from the cliff? (approximate to two decimal places)

Romeo stands $3$ meter away from the wall of Juliet's house. Juliet is standing on the balcony. Romeo raises his eyes $70°$ to look into Juliet's eyes. Romeo and Juliet are both the same height. How high (in meter) is Juliet's balcony?

A boat travels on a bearing of $\mathrm{N}36°\mathrm{W}$ for $25$ km. How many miles north has the boat travelled?  (round off the answer to one decimal place)

A boat travels on a bearing of $\mathrm{N}36°\mathrm{W}$ for $25$ cm. How many miles west has the boat travelled? (round off the answer to one decimal place)

A boat is due south of a lighthouse and sails on a bearing of $292°$ for $51$km until it is due west of the lighthouse. How far (in km) away is it from the lighthouse now? ( round off the answer to one decimal place)

Wally looks out of his office window and sees the top and bottom of an apartment block $300$meter away. The angle of elevation to the top of the office building is $23°$ and the angle of depression to the base of the building is $30°$. How tall (in meter) is the apartment block?

Pierre is standing on the viewing deck of the Eiffel Tower, $300$meter above the ground. He looks down with an angle of depression of $40°$, to see Alain, at point $A$. He looks down a further $32°$ to see Bailee, at point $B$ What is the distance from Alain to Bailee?  (Approximate the answer to its nearest integer)

When you stand at the edge of the Grand Canyon at its deepest point and look horizontally across, the canyon is $498$ meter wide. To look down to the bottom of the canyon from the cliff edge above. you need to move your eyes through an angle of depression of $75°$. When your eyes are $1.5$ meter above the cliff edge, how deep is the Grand Canyon at this point? Answer to the nearest metre.