Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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 \( C. 49^\circ \).

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.