The equation [tex]\cos ^{-1}\left(\frac{3.4}{10}\right)=x[/tex] can be used to determine the measure of angle BAC.

What is the degree measure of angle BAC? Round to the nearest whole degree.

A. [tex]19^{\circ}[/tex]
B. [tex]20^{\circ}[/tex]
C. [tex]70^{\circ}[/tex]
D. [tex]71^{\circ}[/tex]



Answer :

To determine the measure of angle BAC, given the equation [tex]\(\cos^{-1}\left(\frac{3.4}{10}\right) = x\)[/tex], we'll follow these steps:

1. Understand the Equation: The equation [tex]\(\cos^{-1}\left(\frac{3.4}{10}\right) = x\)[/tex] tells us that [tex]\(x\)[/tex] is the angle whose cosine is [tex]\(\frac{3.4}{10}\)[/tex].

2. Calculate the Value of [tex]\(\frac{3.4}{10}\)[/tex]:
[tex]\[ \frac{3.4}{10} = 0.34 \][/tex]

3. Determine the Inverse Cosine (Arccos) of 0.34:
Using the inverse cosine function [tex]\(\cos^{-1}\)[/tex], we find the angle [tex]\(x\)[/tex] in radians:
[tex]\[ x = \cos^{-1}(0.34) \][/tex]

4. Convert Radians to Degrees:
To convert the angle from radians to degrees, use the formula:
[tex]\[ \text{degrees} = x \times \frac{180}{\pi} \][/tex]

5. Round the Result to the Nearest Whole Degree:
Performing these calculations, we find that the degree measure of angle BAC rounds to:
[tex]\[ 70^{\circ} \][/tex]

Therefore, the degree measure of angle BAC is [tex]\( \boxed{70^\circ} \)[/tex].