Question
Rebecca is sketching a right triangle labeled ABC on graph paper. She draws a right angle and labels it A. She draws angle B above angle A, and angle C to the left of angle A. She sketches the hypotenuse of the triangle, a, with a slope of 2/3. Using the inverse of tangent, find the approximate measure of angle C.
41.8 degrees
48.1 degrees
56.3 degrees
33.7 degrees
41.8 degrees
48.1 degrees
56.3 degrees
33.7 degrees
Answers
GPT-4o mini
To find angle C in the right triangle ABC, we can use the slope of the hypotenuse (which is opposite angle C) and the definition of tangent.
The slope of the hypotenuse \( a \) is given as \( \frac{2}{3} \). This means that for every 3 units moved horizontally (along the x-axis), the hypotenuse rises 2 units vertically (along the y-axis).
Therefore, we can express the tangent of angle C as:
\[
\tan(C) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2}{3}
\]
To find the measure of angle C, we need to take the inverse tangent (arctan) of the slope:
\[
C = \tan^{-1}\left(\frac{2}{3}\right)
\]
Now we can use a calculator to compute this:
\[
C \approx \tan^{-1}(0.6667) \approx 33.7 \text{ degrees}
\]
Thus, the approximate measure of angle C is:
**33.7 degrees.**
The slope of the hypotenuse \( a \) is given as \( \frac{2}{3} \). This means that for every 3 units moved horizontally (along the x-axis), the hypotenuse rises 2 units vertically (along the y-axis).
Therefore, we can express the tangent of angle C as:
\[
\tan(C) = \frac{\text{opposite}}{\text{adjacent}} = \frac{2}{3}
\]
To find the measure of angle C, we need to take the inverse tangent (arctan) of the slope:
\[
C = \tan^{-1}\left(\frac{2}{3}\right)
\]
Now we can use a calculator to compute this:
\[
C \approx \tan^{-1}(0.6667) \approx 33.7 \text{ degrees}
\]
Thus, the approximate measure of angle C is:
**33.7 degrees.**