# trig evaluate

• Dec 6th 2006, 12:45 PM
jarny
trig evaluate
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.
• Dec 6th 2006, 12:50 PM
topsquark
Quote:

Originally Posted by jarny
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.

Hmmm...I'm getting 25.6589 degrees, but as you need it to the nearest degree we both agree. (Our calculators may not be calculating it in exactly the same way which might account for the difference.)

-Dan