Question

Question #8ea96

Answer 1

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

(c) `168.72` feet

(d) Triangles are similar and not congruent.

Explanation:

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.