Find the value of x. Round to the nearest tenth. See Problem 2. 14. 15. 16. 17. 18. 19. square

To solve this problem, we will use trigonometric ratios. The trigonometric ratios are sine (sin), cosine (cos), and tangent (tan). They are defined as follows for a right-angled triangle:<br /><br />sin(θ) = opposite/hypotenuse<br />cos(θ) = adjacent/hypotenuse<br />tan(θ) = opposite/adjacent<br /><br />Let's solve for each picture:<br /><br />Picture 1: <br />Here, we have the hypotenuse and an angle, and we need to find the adjacent side. So, we will use the cosine ratio.<br />cos(35) = x/20<br />Rearranging for x gives: x = 20*cos(35)<br /><br />Picture 2: <br />Here, we have the adjacent side and an angle, and we need to find the opposite side. So, we will use the tangent ratio.<br />tan(41) = x/11<br />Rearranging for x gives: x = 11*tan(41)<br /><br />Picture 3: <br />Here, we have the opposite side and an angle, and we need to find the adjacent side. So, we will use the tangent ratio.<br />tan(64) = 7/x<br />Rearranging for x gives: x = 7/tan(64)<br /><br />Picture 4: <br />Here, we have the adjacent side and an angle, and we need to find the hypotenuse. So, we will use the cosine ratio.<br />cos(36) = 10/x<br />Rearranging for x gives: x = 10/cos(36)<br /><br />Now, let's calculate the values:<br /><br />Picture 1: x = 20*cos(35) = 16.4 (rounded to the nearest tenth)<br />Picture 2: x = 11*tan(41) = 9.4 (rounded to the nearest tenth)<br />Picture 3: x = 7/tan(64) = 3.1 (rounded to the nearest tenth)<br />Picture 4: x = 10/cos(36) = 12.4 (rounded to the nearest tenth)<br /><br />So, the values of x for each picture are 16.4, 9.4, 3.1, and 12.4 respectively.