Question #8ea96

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Answer 1 · 2016-06-07T05:06:28

(a) ${19.03}^{o}$ $19.03^o$ (b) $15.34$ $15.34$ feet

(c) $168.72$ $168.72$ feet

(d) Triangles are similar and not congruent.

Let the angle of elevation be $θ$ $theta$ .

It is apparent from the figure that $tan θ = \frac{5}{14.5} = \frac{10}{29} = 0.3448$ $tantheta=5/14.5=10/29=0.3448$

And from tables $θ = {19.03}^{o}$ $theta=19.03^o$

Distance between their shoes can be found using Pythagoras theorem.

and it is $\sqrt{5^{2} + {14.5}^{2}} = \sqrt{25 + 210.25}$ $sqrt(5^2+14.5^2)=sqrt(25+210.25)$

= $\sqrt{235.25} = 15.34$ $sqrt235.25=15.34$ feet

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

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

$\frac{d}{55} = \frac{1}{{sin 19.03}^{o}} = 3.0675$ $d/55=1/(sin19.03^o)=3.0675$

Hence $d = 55 \times 3.0675 = 168.72$ $d=55xx3.0675=168.72$ feet

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