Solve for xx. Round to the nearest tenth of a degree, if necessary

Question

asked Feb 19, 2024 153k views

1 Answer

SteveP · Answer 1 · 2024-02-24T09:50:55+0000

Answer:

x = 55°

Explanation:

Given:

To find:

x° = ?

Solution:

The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse of a right triangle.

$\sf cos (x) = (adjacent )/( hypotenuse)$

In this case, the adjacent side is 5.1 and the hypotenuse is 8.9.

Therefore, the cosine of angle x is:

$\sf cos(x) =(OP)/(OQ)\\\\ =( 5.1)/(8.9)\\\\ = 0.5730337078651$

To find the angle x in degrees, we can use the following formula:

$\sf angle( x )= cos^(-1)(cos x)$

$\sf angle( x )= cos^(-1)( 0.5730337078651 )$

$\sf angle( x ) = 55.037952471005$

In nearest tenth

$\sf angle( x ) \approx 55.0$

Therefore, the angle x is 55°