The towns A, B, and C are shown in the diagram below. The distance between A and B is 11 km. The distance between B and C is 8 km. The angle at C is a right angle. (i) Write down the length of the hypotenuse of the triangle ABC. Hypotenuse = The angle X is marked in the diagram. (ii) Write down the length of the side opposite the angle X. Opposite = (iii) Find sin X. (iv) Use your answer to (iii) to find the size of the angle X. Give your answer correct to the nearest degree.

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The towns A, B, and C are shown in the diagram below - Junior Cycle Mathematics - Question 12 - 2014

Question 12

The towns A, B, and C are shown in the diagram below. The distance between A and B is 11 km. The distance between B and C is 8 km. The angle at C is a right angle... show full transcript

Worked Solution & Example Answer:The towns A, B, and C are shown in the diagram below - Junior Cycle Mathematics - Question 12 - 2014

Step 1

Write down the length of the hypotenuse of the triangle ABC.

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Answer

Hypotenuse = 11 km

Step 2

Write down the length of the side opposite the angle X.

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Answer

Opposite = 8 km

Step 3

Find sin X.

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Answer

To find sin X, we use the formula:

sin X = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{8}{11}

Step 4

Use your answer to (iii) to find the size of the angle X.

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Answer

To find angle X, we use the inverse sine function:

X = \sin^{-1}(\frac{8}{11}) \approx 47^{\circ} \text{ (correct to the nearest degree)}

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