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Answer 1 · 2016-06-07T05:06:28

(a) #19.03^o# (b) #15.34# feet

(c) #168.72# feet

(d) Triangles are similar and not congruent.

Let the angle of elevation be #theta#.

It is apparent from the figure that #tantheta=5/14.5=10/29=0.3448#

And from tables #theta=19.03^o#

Distance between their shoes can be found using Pythagoras theorem.

and it is #sqrt(5^2+14.5^2)=sqrt(25+210.25)#

= #sqrt235.25=15.34# feet

As the building is #50# feet high and Tina is #5# feet high and top of hill is #55# feet high from bottom of hill.

Considering uniformly sloping hill, if distance from bottom to top (along the incline and not horizontal distance) is #d#

#d/55=1/(sin19.03^o)=3.0675#

Hence #d=55xx3.0675=168.72# feet

As all the angles of the two triangles are equal but dimensions are different, they are similar and not congruent.