Question

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?

Answer 1

`color(blue)(A = 3.34925)`

Explanation:

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`