Triangle unknown side length and angles ?

[Kieran]

Line ab is a common base to two triangles - cab and pab. Point p is the top vertex of the smaller triangle and is located "near" the center of the larger triangle. We aren't told if p is a center point or not. ab is 150 cms long , ang cap = 37, ang pab = 43 and ang pba = 50 . Find dist pa , pc and ang acb ? Ang apb is 87 (obviously) and the total angle @ p is 360. So ang apc + bpc = 273 . I can find ap and bp using the sine rule. Could the law of cosines be used ? Thanks.

 

[Deleted member 4993]

Line ab is a common base to two triangles - cab and pab. Point p is the top vertex of the smaller triangle and is located "near" the center of the larger triangle. We aren't told if p is a center point or not. ab is 150 cms long , ang cap = 37, ang pab = 43 and ang pba = 50 . Find dist pa , pc and ang acb ? Ang apb is 87 (obviously) and the total angle @ p is 360. So ang apc + bpc = 273 . I can find ap and bp using the sine rule. Could the law of cosines be used ? Thanks.

Law of cosines can be used when you know the measures of:

any two sides of the triangle and

the included angle between those two sides.