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? asked in Science & MathematicsMathematics · 3 years ago

Trigonometry help?

I was absent when my class learnt about the sine and cosine rule

I've been told how it works

(sine rule is sinA/a=sinB/b and so on etc and cosine rule is a²=b²+c²-bcsinA)

I also know pythagoras and the SOH CAH TOA thing

However, I think I'm missing something, because now I'm stuck on my homework

I am given two angles (let's call them B and C) and the line connecting them (let's call it a)

I'm meant to find the height between c and the line a which I'm going to do with pythagoras, but for that I need the length of side b or c.

Please help

PS. I am naming these angles and sides not based on Pythagoras, but by cosine and sine rule. Therefore side C might not be the hypotenuse

Update:

Yes, i got the cosine rule wrong. Replace the sin with cos. Sorry, that was my fault

3 Answers

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  • ?
    Lv 7
    3 years ago
    Favorite Answer

    Pythagoras is applicable and can be used ONLY if you are dealing with a right triangle. If the sum of the given angles, B and C, is 90° or if B or C is 90°, then and only then would Pythagoras be useful. However, you have enough to solve the triangle without Pythagoras.

    With the convention that side a is opposite angle A, b is opposite B, and c is opposite C. you have all three angles: B and C are given and since the sum of the three angles of a plane triangle is always 180°, A = 180 - (B+C) . Then you simply use the Law of Sines to get the unknown sides.

    A, B, and C are known: B and C are given and A = 180°-(B+C)

    c is given

    b = c(sinB/sinC)

    a = c(sinA/sinC)

    Apparently what you are "missing" is the sum of angles in a plane triangle is always 180°. That allows you to calculate the third angle of a triangle when you know two of them.

  • ?
    Lv 7
    3 years ago

    You seem to be mixing up your upper and lower case letters.

    First you use "B" and "C" as vertices/angles and "a" as the side, which is fine.

    But then you want to find height between "c" and line "a".

    This doesn't make sense. If "c" is a side of triangle, then it must intersect "a", so distance is 0. If you meant vertex "C", then it is one of the endpoints of line "a", so again distance is 0. Perhaps you meant distance between vertex "A" and opposite side "a"?

    Also, you then say that "side C" might not be the hypotenuse. But "C" is a vertex, not a side. You meant that "side c" might not be the hypotenuse.

    I see you are aware of the mistake in Cosine Rule (should be cosA, not sinA). But there is a 2nd mistake you didn't catch: there should be a 2 in front of bc cosA

    a² = b² + c² − 2bc cosA

    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    Anyway, in triangle ABC with opposite sides a, b, c, respectively, we are given a, B, and C

    But since angles of triangle add up to 180, we can easily find A = 180 − B − C

    So now we have a, A, B, and C. We can find b and c using Law of Sines:

    b/sinB = a/sinA ----> b = a * sinB/sinA

    c/sinC = a/sinA ----> c = a * sinC/sinA

  • ?
    Lv 6
    3 years ago

    cosine rule is a²=b²+c²-bc cos (not sin) A

    With <B and <C given you can solve for <A (180 - <B - <C) assuming this is a triangle or you can form one.

    Then with sin rule you can solve for the other sides.

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