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Trigonometry or Pythagoras

Hey, I have the question below and I was just wondering if someone could help me out, I'm confused because I don't think you use trigonometric functions to solve it, but I wanted to know if my answer using Pythagoras is correct.

a^2+b^2=c^2
150^2+120^2=c^2
36900=c^2
(Square Root of) 36900 = c
c = 192m (to the nearest metre)
?

Reply 1

the bear

if a,b,c are the sides of a right angled triangle and c is the longest side then it looks good

Reply 2

username5118974

Original post by the bear

if a,b,c are the sides of a right angled triangle and c is the longest side then it looks good

this is the triangle, it isnt right angled so I'm unsure?

Reply 3

the bear

Original post by Kakakaty

this is the triangle, it isnt right angled so I'm unsure?

there is not a right angle, so Pythagoras won't help you

Reply 4

username5118974

FB = 150m
BG = 120m
FG^2=150^2+120^2-2(150)(120) cos(86)
FG^2= 34388.7696
FG = (Square Root Of) 34388.7696
FG = 185 (Rounded to the nearest metre)
Is this correct?

Anyone?

Looks ok (right method and ~ans), but not typed the numbers into my calc.

Reply 8

username5118974

Original post by mqb2766

Looks ok (right method and ~ans), but not typed the numbers into my calc.

Thankyou.
For a question like this one would I have to use the Cosine Rule to find angle x?

Reply 9

username5118974

Anyone able to help with ^

Reply 10

the bear

Original post by Kakakaty

Thankyou.
For a question like this one would I have to use the Cosine Rule to find angle x?

the sine rule would be best here

Reply 11

username5118974

Original post by the bear

the sine rule would be best here

How do you figure out which rule would be best to use?

Reply 12

mqb2766

Google it, it's a common question.

Cos works when you have a "<", i.e. know two sides and the angle between them and you want to find the third side. Or you know all three sides and want to find an angle.

Sin works when you know an angle and the opposing side, a and A, say. You also know another side or angle and want to find its opposing angle or side.

(edited 3 years ago)

Reply 13

the bear

Original post by Kakakaty

How do you figure out which rule would be best to use?

you can always try the sine rule first.... if it does not work then switch over to the cosine rule.

Reply 14

Ã„ries

Original post by the bear

you can always try the sine rule first.... if it does not work then switch over to the cosine rule.

Since the angle of 83° isn’t an included angle, you apply sine rule may lead to ambiguous cases. You should test whether an obtuse angle solution is valid.