Question

What is the angle of elevation from her hand up to the kite, and what is the horizontal distance from her hand to directly below the kite? (Round your answers to the nearest tenth)

Answer 1

Check the picture below.

`\sin( \theta )=\cfrac{\stackrel{opposite}{44}}{\underset{hypotenuse}{65}} \implies \sin^(-1)(~~\sin( \theta )~~) =\sin^(-1)\left( \cfrac{44}{65} \right) \\\\\\ \theta =\sin^(-1)\left( \cfrac{44}{65} \right)\implies \boxed{\theta \approx 42.6^o} \\\\[-0.35em] ~\dotfill`

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=√(c^2 - o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{65}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{44} \end{cases} \\\\\\ x=√( 65^2 - 44^2)\implies x=√( 4225 - 1936 ) \implies x=√( 2289 )\implies \boxed{x\approx 47.8}`

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