Questions: Solve the right triangle with a=1.26 and b=17.5. Round off the results according to the table below Measurements of Angle to Nearest Accuracy of Trigonometric Function ------ 1° 2 significant digits 0.1° 3 significant digits 0.01° 4 significant digits Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. A. C= A= B=

Solve the right triangle with a=1.26 and b=17.5. Round off the results according to the table below Measurements of Angle to Nearest Accuracy of Trigonometric Function ------ 1° 2 significant digits 0.1° 3 significant digits 0.01° 4 significant digits Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. A. C= A= B=
Transcript text: Solve the right triangle with $a=1.26$ and $b=17.5$. Round off the results according to the table below \begin{tabular}{cc} \hline \begin{tabular}{c} Measurements of \\ Angle to Nearest \end{tabular} & \begin{tabular}{c} Accuracy of \\ Trigonometric \\ Function \end{tabular} \\ \hline $1^{\circ}$ & 2 significant digits \\ $0.1^{\circ}$ & 3 significant digits \\ $0.01^{\circ}$ & 4 significant digits \\ \hline \end{tabular} Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. A. $C=\quad A=\quad B=$ $\square$ 。
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Solution

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Solution Steps

To solve the right triangle with given sides \(a = 1.26\) and \(b = 17.5\), we need to find the hypotenuse \(c\) and the angles \(A\) and \(B\). We can use the Pythagorean theorem to find \(c\) and trigonometric functions to find the angles.

  1. Use the Pythagorean theorem to find \(c\): \[ c = \sqrt{a^2 + b^2} \]

  2. Use the inverse trigonometric functions to find the angles: \[ A = \arctan\left(\frac{a}{b}\right) \] \[ B = \arctan\left(\frac{b}{a}\right) \]

  3. Convert the angles from radians to degrees.

  4. Round the results according to the given table.

Step 1: Calculate the Hypotenuse

Using the Pythagorean theorem, we find the hypotenuse \(c\) as follows: \[ c = \sqrt{a^2 + b^2} = \sqrt{(1.26)^2 + (17.5)^2} \approx 17.55 \]

Step 2: Calculate Angle \(A\)

To find angle \(A\), we use the tangent function: \[ A = \arctan\left(\frac{a}{b}\right) = \arctan\left(\frac{1.26}{17.5}\right) \approx 4.1^\circ \]

Step 3: Calculate Angle \(B\)

Similarly, angle \(B\) can be calculated using: \[ B = \arctan\left(\frac{b}{a}\right) = \arctan\left(\frac{17.5}{1.26}\right) \approx 85.9^\circ \]

Final Answer

The results for the triangle are: \[ C = 17.55, \quad A = 4.1^\circ, \quad B = 85.9^\circ \] Thus, the final boxed answer is: \[ \boxed{C = 17.55, A = 4.1^\circ, B = 85.9^\circ} \]

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