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 the trigonometric relation

In right - triangle $ABC$ with right - angle at $C$, we know the side $AC = 10$ m and the angle $\angle A=75^{\circ}$, and we want to find the hypotenuse $AB$. We use the cosine function. $\cos(A)=\frac{AC}{AB}$.

Step2: Rearrange the formula to solve for $AB$

From $\cos(A)=\frac{AC}{AB}$, we can rewrite it as $AB=\frac{AC}{\cos(A)}$.

Step3: Substitute the given values

We know that $AC = 10$ m and $A = 75^{\circ}$, and $\cos(75^{\circ})\approx0.259$. Then $AB=\frac{10}{\cos(75^{\circ})}=\frac{10}{0.259}\approx38.6$ m.

Answer:

38.6 m