Question

The equation tan−1 (8.9/7.7) = x can be used to find the measure of angle LKJ.

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

Answer 1

tan−1 (8.9/7.7) = x can also be written as x = arctan (1.156).

Using my TI-83 calculator's inverse tangent function key, I get x = 0.858 radian. This is equivalent to 49.135 degrees, which we must round off to the nearest whole degree: 49 degrees.

Answer 2

Yes, the given equation can be used to find the measure of angle LKJ. The measure of angle LKJ is 49 degree.

Explanation:

It the given figure the triangle LKJ is a right angle triangle. Measure of angle B is 90 degree.

`\tan\theta=(perpendicular)/(base)`

`\tan K=(LJ)/(LK)`

`\tan K=(8.9)/(7.7)`

Using inverse trigonometry property.

`K=\tan^(-1)((8.9)/(7.7))`

Therefore the given equation can be used to find the measure of angle LKJ.

`K=\tan^(-1)(1.15584416)`

`K=49.1346713737\approx 49`

Therefore the measure of angle LKJ is 49 degree.