Answer:
The length of AB is approximately 6.07 m
Step-by-step explanation:
The given dimensions of the triangle are;
The value of x = 7.7 m
The measure of angle, θ = 52°
The length of side AB = Required
The given triangle ΔABC is a right triangle, with the following sides;
AC = x = The hypotenuse (opposite to right angle) side
(Leg) AB = The opposite side to the reference angle, θ
(Leg) BC = The adjacent side to the reference angle, θ
By trigonometric ratio, we have;
![sin(\theta) = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length} = \dfrac{AB}{x}](https://tex.z-dn.net/?f=sin%28%5Ctheta%29%20%3D%20%5Cdfrac%7BOpposite%20%5C%20leg%20%5C%20length%7D%7BHypotenuse%20%5C%20length%7D%20%3D%20%5Cdfrac%7BAB%7D%7Bx%7D)
Therefore;
![sin(52^{\circ}) = \dfrac{AB}{7.7}](https://tex.z-dn.net/?f=sin%2852%5E%7B%5Ccirc%7D%29%20%3D%20%5Cdfrac%7BAB%7D%7B7.7%7D)
AB = 7.7 × sin(52°) ≈ 6.07
The length of AB ≈ 6.07 m.