In the triangle $ABC$, $AB = 16 \text{ cm}, AC = 13 \text{ cm}, \angle ABC = 50^\circ$ and angle $BCA = x^\circ$ - Edexcel - A-Level Maths Pure - Question 3 - 2017 - Paper 3
Question 3
In the triangle $ABC$, $AB = 16 \text{ cm}, AC = 13 \text{ cm}, \angle ABC = 50^\circ$ and angle $BCA = x^\circ$.
Find the two possible values for $x$, giving your a... show full transcript
Worked Solution & Example Answer:In the triangle $ABC$, $AB = 16 \text{ cm}, AC = 13 \text{ cm}, \angle ABC = 50^\circ$ and angle $BCA = x^\circ$ - Edexcel - A-Level Maths Pure - Question 3 - 2017 - Paper 3
Step 1
Find the value of $\sin x$ using the sine rule
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Answer
Using the sine rule, we know that:
sinAa=sinBb
In this case, let:
a=16 cm (opposite to angle ACB=x)
b=13 cm (opposite to angle ABC=50∘)
Thus,
sinx16=sin50∘13
Rearranging gives:
sinx=16×13sin50∘
Step 2
Calculate $\sin 50^\circ$
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Answer
Using a calculator, we find:
sin50∘≈0.7660
Substituting this value in gives:
sinx=16×130.7660≈0.9430
Step 3
Find possible values of $x$
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Now, we need to determine the angle x:
The first possible value of x can be found using the inverse sine function:
x=sin−1(0.9430)≈70.5∘
The second possible value of x can be calculated as follows:
x=180∘−70.5∘=109.5∘
Thus, the two possible values for x are approximately:
