Answer to Question #178916 in Trigonometry for Raine

Question

1. Pont du Gard, an ancient Roman aqueduct bridge built in the first century AD in France, is approximately 49 m high. Alice  and Bob are standing 75 apart taking pictures of the bridge. From Alice, the angle of elevation to the top of the bridge is 37 degree;  from Bob, the angle of elevation to the top of the bridge is 29 degree.

Determine the angle, to the nearest degree, that is formed between Alice, the base of the bridge, and Bob. Label the diagram  with the given dimensions and show all your work to receive full marks.

Answer 1

$tan\theta$ $=\frac{opp}{adj}$

tan $37\degree=$ $\frac{x}{m}$

x=m tan$37\degree$

tan 29$\degree$ =$\frac{x}{m+75}$

x=m+75tan 29$\degree$

m tan37$\degree$ =m+75tan29$\degree$

Get the value of m assuming m=27

x=m tan37$\degree$

x=27tan37$\degree$ But assuming x=21m

Therefore:

(49-x)=(49-21)=28m

Angle between Alice and base:

tan$\alpha=\frac{opp}{adj}$

$tan\alpha=\frac{28}{27}$

$\alpha$ =tan^-1$(\frac{28}{27})$

=$46.04\degree$

Angle between Bob and the base

tan$\beta=\frac{28}{27+75}$

=$\frac{28}{102}$

β=tan^-1$(\frac{28}{102})$

$=15.35\degree$