Use the image to answer the question.

Question

A right triangle upper A upper B upper C. The right angle, labeled B, is on the bottom left. The hypotenuse, side upper A upper C, slopes downward left to right. All sides are assigned values.

Use the inverse of tangent to solve for the approximate angle measure of vertex C , rounded to the nearest whole degree.

(1 point)
Responses

53°
53°

37°
37°

39°
39°

59°

Answer 1

To find the angle measure of vertex C in a right triangle (triangle ABC) using the inverse tangent function (also known as arctan), we need the lengths of the sides of the triangle around that angle.

Assuming we have the lengths:

• The side opposite angle C (let's call it BC)
• The side adjacent to angle C (let's call it AB)

The formula to find angle C using the inverse tangent is:

$$C=\arctan \left(\frac{\text{opposite}}{\text{adjacent}}\right)=\arctan \left(\frac{BC}{AB}\right)$$

You would plug in the numerical values for BC and AB to compute the angle C. Without specific side lengths provided in the image you mentioned, I cannot calculate it directly. However, you can apply the formula accordingly.

If you've already calculated the angle and are choosing from the given responses, here’s how you could reason:

• If $C$ approximately calculates to 37°, 39°, 53°, or 59°, select the closest one to what you computed.

Without the side lengths or calculations being visible, I suggest you double-check the triangle's side lengths and use the inverse tangent function to get the angle. If you need help with the calculations or have further information, feel free to provide it!