# Trig: A triangle has a side of length 1, a side of length 4 and an angle of 30◦

#### s179

##### New member
3. A triangle has a side of length 1, a side of length 4 and an angle of 30◦.

(a) Explain carefully why there are precisely two possible such triangles. [7 marks]
(b) In each case determine the third side length and the other two angles of the triangle.[28 marks]

so i calculated the two angles for triangle 1 and found them to be 7.18 and 142.82. ive tried calculating the angles for triangle 2 and keep getting a negative angle, not sure what im doing.

#### tkhunny

##### Moderator
Staff member
What you have not stated is where the angle is in relation to the two sides. I'm guessing the angle is NOT between the two sides, but you didn't say that.

Please show your layout. How did you conclude what you have concluded?

Do you know that $$\displaystyle sin(\alpha) = \sin(\pi - \alpha)$$?

#### Dr.Peterson

##### Elite Member
3. A triangle has a side of length 1, a side of length 4 and an angle of 30◦.

(a) Explain carefully why there are precisely two possible such triangles. [7 marks]
(b) In each case determine the third side length and the other two angles of the triangle.[28 marks]

so i calculated the two angles for triangle 1 and found them to be 7.18 and 142.82. ive tried calculating the angles for triangle 2 and keep getting a negative angle, not sure what im doing.