In questions 1-11 \(\Delta \mathrm{ABC}\) has a right angle at \(\mathrm{C}\). Calculate \(A\) given \(\mathrm{AC}=14 \mathrm{~cm}\) and \(\mathrm{BC}=9 \mathrm{~cm}\)

Short Answer

Expert verified
Answer: The measure of angle A in the right-angled triangle ΔABC is approximately 32.73°.

Step by step solution

01

Identify the given measurements

We are given the measurements of two sides in a right-angled triangle: - AC = 14 cm (adjacent side) - BC = 9 cm (opposite side)
02

Use the inverse tangent function

The inverse tangent (arctan) function is used to find the angle A, using the formula: A = arctan(opposite side / adjacent side) In our case, we have: A = arctan(BC / AC)
03

Plug the values and calculate angle A

Now, we can substitute the given side measurements into the formula: A = arctan(9 cm / 14 cm) Calculate the angle using a calculator: A ≈ 32.73°
04

Write the final answer

The measure of angle A in the right-angled triangle ΔABC is approximately 32.73°.

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