Question: Here is a different triangle.
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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