Here is a different triangle. Leah tries to use the sine rule to work out the size of angle x. What error has she made in this working?

Question: Here is a different triangle.

83001H

Leah tries to use the sine rule to work out the size of angle x.
Here are the first two lines of her working.
x/sin31 = 54/sin72
x = 54sin31/sin72.
What error has she made in this working?

Answer : x = sin-1(31sin72/54)

Explanation: Sine Rule of Triangle

The sine rule, also known as the law of sines, is a fundamental concept in trigonometry that applies to any triangle, whether it is acute, obtuse, or right-angled. The rule states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. This can be expressed mathematically as:
a/sin(A) = b/sin(B) = c/sin(C)
Where:

  • a, b, and c are the lengths of the sides of the triangle
  • A, B, and C are the opposite angles

This rule is often used to solve for unknown angles or sides in a triangle when some of the other angles or sides are known.

Now, Using the rule in the given triangle

31/sin(x) = 54/sin(72)
sin(x) = 31sin(72)/54

x = sin-1(31sin72/54)

Leah taken the wrong angle.

83001H

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