SOLUTION: A 52​-ft-wide house has a roof with a 6​-12 pitch​ (the roof rises 6 ft for a run of 12​ ft). The owner plans a 18​-ft-wide addition that will have a

Algebra ->  Trigonometry-basics -> SOLUTION: A 52​-ft-wide house has a roof with a 6​-12 pitch​ (the roof rises 6 ft for a run of 12​ ft). The owner plans a 18​-ft-wide addition that will have a       Log On


   

Question 1131839: A 52​-ft-wide house has a roof with a 6​-12 pitch​ (the roof rises 6 ft for a run of 12​ ft). The owner plans a 18​-ft-wide addition that will have a 3​-12 pitch to its roof. Find the lengths of AB overbar and BC overbar in the accompanying figure.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


tan%28gamma%29=6%2F12
gamma=tan%5E-1%286%2F12%29
gamma=26.57°

tan%28alpha%29=3%2F12
alpha=tan%5E-1%283%2F12%29
alpha=14.04°

beta=180-gamma°
beta=180-26.57°
beta=153.43°


delta=180-%28beta%2Balpha%29°
delta=180-%28153.43%2B14.04%29°
delta=180-167.47°
delta=12.53°


AB%2Fsin%28153.43%29=14%2Fsin%2812.53%29
AB=14sin%28153.43%29%2Fsin%2812.53%29
AB=6.26207%2F0.216951
AB≈28.9ft


BC%2Fsin%2814.04%29=14%2Fsin%2812.53%29
BC=14sin%2814.04%29%2Fsin%2812.53%29
BC=3.39639%2F0.216951
BC≈+15.7ft