I have a right triangle where side b=12 (longer side) and the adjacent angle to that side is 30 degrees. I need the find the hypotenuse and side a (the shortest side). Can someone please explain how to use the formula for a 30-60-90 triangle to solve for the hypotenuse and the shortest side. Also show work to solve the problem.
-
SOHCAHTOA
sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent
cos 30 = 12 / hypotenuse
(cos 30) * hypotenuse = 12
hypotenuse = 12 / cos 30
hypotenuse = 12 / ((√3)/2)
hypotenuse = (12/1) / ((√3)/2)
hypotenuse = (12/1) * (2/√3)
hypotenuse = 24 / √3
hypotenuse = 24√3 / √3√3
hypotenuse = 24√3 / 3
hypotenuse = 8√3
tan 30 = a / 12
12 * tan 30 = a
12 * (1/√3) = a
12 / √3 = a
12√3 / √3√3 = a
12√3 / 3 = a
4√3 = a
sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent
cos 30 = 12 / hypotenuse
(cos 30) * hypotenuse = 12
hypotenuse = 12 / cos 30
hypotenuse = 12 / ((√3)/2)
hypotenuse = (12/1) / ((√3)/2)
hypotenuse = (12/1) * (2/√3)
hypotenuse = 24 / √3
hypotenuse = 24√3 / √3√3
hypotenuse = 24√3 / 3
hypotenuse = 8√3
tan 30 = a / 12
12 * tan 30 = a
12 * (1/√3) = a
12 / √3 = a
12√3 / √3√3 = a
12√3 / 3 = a
4√3 = a
-
first know about these formulae: sine=perpendicular/hypotenuse. Assuming that the side b is the perpendicular to side a and angle x= 30 degrees, use this: sine 30=1/2, thus 1/2=perpendicular/hypotunuse i.e. 12/h. Now i guess the answer is 24 i guess....
-
You probably shouldn't fall asleep during class.
-
sine 30 = .5 =hyp/a ,so hyp = 2a
4a^2 =a^2 +12^2
3a^2 =144
a^2 = 48
a =6.9282 and hyp = 13.8564
4a^2 =a^2 +12^2
3a^2 =144
a^2 = 48
a =6.9282 and hyp = 13.8564