Question
Find the measure of θ
. Round your answer to the nearest whole number.
2 cm
5 cm
(1 point)
degrees
. Round your answer to the nearest whole number.
2 cm
5 cm
(1 point)
degrees
Answers
GPT-4o mini
To find the measure of angle \( \theta \) in a triangle with sides of lengths 2 cm and 5 cm, we need more information, such as the length of the third side or any angle measures.
However, if we assume that you are referring to a right triangle where these lengths represent the two legs, we can apply trigonometric ratios. Assuming \( \theta \) is the angle opposite the 2 cm side, we can use the sine, cosine, or tangent functions.
### Using Tangent
If we assume a right triangle with 2 cm opposite \( \theta \) and 5 cm as the adjacent side:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2}{5}
\]
To find \( \theta \), we take the arctan:
\[
\theta = \tan^{-1}\left(\frac{2}{5}\right)
\]
Calculating this using a calculator:
\[
\theta \approx 21.8^\circ
\]
Rounding to the nearest whole number, \( \theta \approx 22^\circ \).
Please clarify if the triangle has different conditions or if further information is needed!
However, if we assume that you are referring to a right triangle where these lengths represent the two legs, we can apply trigonometric ratios. Assuming \( \theta \) is the angle opposite the 2 cm side, we can use the sine, cosine, or tangent functions.
### Using Tangent
If we assume a right triangle with 2 cm opposite \( \theta \) and 5 cm as the adjacent side:
\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2}{5}
\]
To find \( \theta \), we take the arctan:
\[
\theta = \tan^{-1}\left(\frac{2}{5}\right)
\]
Calculating this using a calculator:
\[
\theta \approx 21.8^\circ
\]
Rounding to the nearest whole number, \( \theta \approx 22^\circ \).
Please clarify if the triangle has different conditions or if further information is needed!