A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2# and the angle between sides B and C is #pi/12#. If side B has a length of 5, what is the area of the triangle?

1 Answer
Feb 21, 2016

#color(blue)(A = 3.34925)#

Explanation:

enter image source here

NOTE: Diagram drawn not to scale

Sorry for my bad drawing :D

Angles in Uppercase Letters (A, B, C)
Sides in Lowercase Letters (a, b, c)

Angle #C = pi/2#

Angle #A = pi/12#

to convert radian values to degrees, we simply multiply it by #180/pi#

Angle #C = pi/2 * 180/pi = (180cancelpi)/(2cancelpi)#

Angle #C= 90^o#

Angle #A = pi/12 * 180/pi = (180cancelpi)/(12cancelpi)#

Angle #A = 15^o#

Side #b = 5#

we must get the value of Side #a# to get the area of triangle,

we can use trigonometric functions to get the value of side of the triangle and apply algebraic techniques to find the value of #a#.

#tan 15^o = a/5#

#5tan15^o = a#

#a = 5tan15^o#

#a = 1.3397#

Since the formula for Area of Triangle is,

#Area = 1/2bh#

where #b# = base can be the side #a#, and #h = #height can be the side #b#.

Plugging All Variables,

#Area = 1/2(1.3397)(5)#

#Area = 3.34925#