Answer:
x = 30.6 ft
A = 58.1°
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
As the triangle is a right triangle, use Pythagoras Theorem to find length x.
[tex]\implies x^2+19^2=36^2[/tex]
[tex]\implies x^2+361=1296[/tex]
[tex]\implies x^2=935[/tex]
[tex]\implies x=\sqrt{935}[/tex]
[tex]\implies x=30.6\; \sf ft \;\; (3\;s.f.)[/tex]
[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the given right triangle:
- θ = A
- A = 19.0 ft
- H = 36.0 ft
Substitute the values into the formula and solve for A:
[tex]\implies \sf \cos A=\dfrac{19.0}{36.0}[/tex]
[tex]\implies \sf A= \cos^{-1}\left(\dfrac{19}{36}\right)[/tex]
[tex]\implies \sf A=58.1^{\circ}\;\;(3\;s.f.)[/tex]
