Question

what is the length of $overline{ab}$? round to the nearest tenth.
c
10 m
75°
a
x
b
9.7 m
10.4 m
37.3 m
38.6 m

Explanation:

Step1: Identify triangle type and sides

Right triangle at C, AB is hypotenuse, AC=10m (adjacent to 75°).

Step2: Apply cosine ratio

$\cos(75^\circ) = \frac{AC}{AB} \implies AB = \frac{AC}{\cos(75^\circ)}$

Step3: Calculate AB

$AB = \frac{10}{\cos(75^\circ)} \approx \frac{10}{0.2588} \approx 38.6$

Answer:

D. 38.6 m