Can someone check my work and logic for this word problem: Two ladders, one of which is twice as long as the other, each having one end resting on the floor, have their opposite ends reaching the same vertical height along a wall. The shorter ladder makes a 60 degree angle with the floor. What angle (to the nearest degree) does the longer ladder make with the floor? Let x=the height, h = the hypotenuse, and θ= the degree of triangle 2.
1. Sin60=x/h 2. Sinθ=x/(2h) Set both equal to one so:
(Sin60*h)/x = 1 = (sinθ*2h)/x
Eliminate the one since both equal one and the same with x because they both have a common denominator. Sin60*h=Sinθ*2h. Divide so:
Sin60/Sinθ=2h/h so 2=Sin60/Sinθ. Switch 2 and Sinθ so Sinθ=Sin60/2. This means (Sin^(-1))(Sin60/2) which equals 25.91 degrees.