Question

Please help! I’m having a hard time understanding these two questions

1.)
Joel is 6 ft tall. He notices that the distance from the top of his head to the tip of his shadow is 16 ft. What is the measure x of the angle that his shadow makes with the hypotenuse of the right triangle? Round the angle measure to the nearest whole number degree.
(Use an inverse trig function)

2.)
Which formula (Pythagorean Theorem) can be used to find length of Joel’s shadow?

A.) 6^2 + x^2 + 16^2
B.) 6^2 + x^2 = 16^2
C.) 6^2 + 16^2 = x^2
D.) x^2 + 16^2 = 6^2

Answer 1

`\sin( x )=\cfrac{\stackrel{opposite}{6}}{\underset{hypotenuse}{16}} \implies \sin( x )=\cfrac{3}{8}\implies x=\sin^(-1)\left( \cfrac{3}{8} \right)\implies \boxed{x\approx 22^o} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{16}\\ a=\stackrel{adjacent}{x}&\leftarrow \textit{Joel's shadow}\\ o=\stackrel{opposite}{6} \end{cases}`

`(16)^2= (x)^2 + (6)^2\implies \boxed{6^2+x^2=16^2}\implies x^2=16^2-6^2 \\\\\\ x=√(16^2-6^2)\implies x=√(220)\implies \boxed{x\approx 14.83}~ft`

Make sure your calculator is in Degree mode.