Question

what is the length of $overline{ab}$? round to the nearest tenth.

9.7 m
10.4 m
37.3 m
38.6 m

Explanation:

Step1: Identify adjacent side & angle

We have a right triangle, with $\angle A = 75^\circ$, adjacent side $AC = 10$ m, and $AB$ (labeled $x$) is the hypotenuse.

Step2: Use cosine trigonometric ratio

The cosine of an angle in a right triangle is $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$. Substitute values:
$\cos(75^\circ) = \frac{10}{x}$

Step3: Rearrange to solve for $x$

Rearrange the formula to isolate $x$:
$x = \frac{10}{\cos(75^\circ)}$

Step4: Calculate the value

$\cos(75^\circ) \approx 0.2588$, so:
$x \approx \frac{10}{0.2588} \approx 38.6$

Answer:

D. 38.6 m