(Solved): 4) A ladder that is \\( 4 \\mathrm{~m} \\) long is leaning in the corner as shown. If the ladder ma ...

4) A ladder that is \\( 4 \\mathrm{~m} \\) long is leaning in the corner as shown. If the ladder makes a \\( 60^{\\circ} \\) angle with the ground, use trigonometry to find the height of the top of the ladder. 5) Use trigonometry to find the distance between the bottom of the ladder and the corner. 6) Show that your answers to 4 and 5 obey the Pythagorean theorem.