What is the length of ab ? round to the nearest tenth. 9.7 m 10.4 m 37.3 m 38.6 m

The length of AB to the nearest tenth is; D: 38.6 m

Trigonometric Ratios

We see that the triangle ABC is a right angle triangle.

Thus, we can use trigonometric ratio to solve it.

Thus;

AC/AB = cos 75

we have AC = 10.

Thus;

10/AB = 0.2588

AB = 10/0.2588

AB = 38.64

Approximating to the nearest tenth gives;

AB = 38.6 m

Read more about trigonometric ratios at; link

The only way you can find x here is to use a trig ratio.  We have the reference angle of 75, CA is 10 which is the side adjacent to the reference angle, and we are looking for the hypotenuse.  The ratio that relates the side adjacent to a reference angle to the hypotenuse is cosine.  Therefore, .  Solving for x we get .  Do that on your calculator and find that the hypotenuse is 38.6 m long, last choice from above.