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The equation [tex] \tan ^{-1}\left(\frac{8.9}{7.7}\right)=x [/tex] can be used to find the measure of angle [tex]$LKJ$[/tex].

What is the measure of angle [tex]$LKJ$[/tex]? Round to the nearest whole degree.

A. [tex]$41^{\circ}$[/tex]
B. [tex]$45^{\circ}$[/tex]
C. [tex]$49^{\circ}$[/tex]
D. [tex]$55^{\circ}$[/tex]

Sagot :

GinnyAnswer
To find the measure of angle [tex]\( LKJ \)[/tex] given the equation [tex]\(\tan^{-1}\left(\frac{8.9}{7.7}\right) = x\)[/tex], follow these steps:

1. Calculate the Ratio:
[tex]\[ \frac{8.9}{7.7} \][/tex]

2. Find the Inverse Tangent:
Using a calculator or trigonometric tables, find [tex]\(\tan^{-1}(8.9 / 7.7)\)[/tex]. This will give you the angle [tex]\( x \)[/tex] in radians.

3. Convert from Radians to Degrees:
Once you have the angle in radians, convert it to degrees. The conversion factor is [tex]\(\frac{180}{\pi}\)[/tex] degrees per radian.

4. Round to the Nearest Whole Degree:
After converting the angle to degrees, round the result to the nearest whole number.

Following these steps, you will find:

1. The ratio [tex]\(\frac{8.9}{7.7}\)[/tex] is approximately [tex]\(1.155844155844156\)[/tex].

2. The inverse tangent [tex]\(\tan^{-1}(1.155844155844156)\)[/tex] is approximately [tex]\(0.857561792357106\)[/tex] radians.

3. Converting [tex]\(0.857561792357106\)[/tex] radians to degrees:
[tex]\[ 0.857561792357106 \times \frac{180}{\pi} \approx 49.13467137373643 \text{ degrees} \][/tex]

4. Rounding [tex]\(49.13467137373643\)[/tex] degrees to the nearest whole number gives [tex]\(49\)[/tex] degrees.

Therefore, the measure of angle [tex]\( LKJ \)[/tex] is [tex]\( \boxed{49^{\circ}} \)[/tex].
thapa63

Answer:

To find the measure of angle \( L K J \) using the equation

\[

\tan^{-1}\left(\frac{8.9}{7.7}\right) = x,

\]

we need to calculate the value of \( x \).

First, calculate the ratio:

\[

\frac{8.9}{7.7} \approx 1.15584.

\]

Now, find \( \tan^{-1}(1.15584) \) using a calculator or inverse tangent function. This gives:

\[

x \approx 49.4^\circ.

\]

Rounding to the nearest whole degree, we get:

\[

x \approx 49^\circ.

\]

Therefore, the measure of angle \( L K J \) is \( C. 49^\circ \).

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