Question
Use the inverse of the tangent ratio to find the approximate measure of the missing angle. Round your answer to the nearest whole degree.
2cm,5cm
2cm,5cm
Answers
GPT-4o mini
To find the measure of the missing angle using the inverse tangent (arctan) function, we can use the formula:
\[
\theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right)
\]
In a right triangle, if we have a side of 2 cm and another side of 5 cm, we can assume the sides correspond to the opposite and adjacent sides relative to the angle we are finding.
1. Let's assume:
- Opposite side = 2 cm
- Adjacent side = 5 cm
2. Now, plug these values into the equation:
\[
\theta = \tan^{-1}\left(\frac{2}{5}\right)
\]
3. Calculate this value:
Using a calculator, we can find:
\[
\theta \approx \tan^{-1}(0.4) \approx 21.8^\circ
\]
4. Rounding this to the nearest whole degree gives us:
\[
\theta \approx 22^\circ
\]
Thus, the approximate measure of the missing angle is **22 degrees**.
\[
\theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right)
\]
In a right triangle, if we have a side of 2 cm and another side of 5 cm, we can assume the sides correspond to the opposite and adjacent sides relative to the angle we are finding.
1. Let's assume:
- Opposite side = 2 cm
- Adjacent side = 5 cm
2. Now, plug these values into the equation:
\[
\theta = \tan^{-1}\left(\frac{2}{5}\right)
\]
3. Calculate this value:
Using a calculator, we can find:
\[
\theta \approx \tan^{-1}(0.4) \approx 21.8^\circ
\]
4. Rounding this to the nearest whole degree gives us:
\[
\theta \approx 22^\circ
\]
Thus, the approximate measure of the missing angle is **22 degrees**.