To find the length of AB, we can use the concept of trigonometry and the given information.
First, let's label the given information. P8 represents point P, which is not relevant to finding the length of AB. 8 m represents the length of a side of the triangle, and 80° represents the angle opposite to side AB.
To find the length of AB, we can use the trigonometric function cosine (cos). Cosine relates the adjacent side and the hypotenuse of a right triangle.
In this case, side AB is adjacent to angle 80°, and the hypotenuse is the given side length of 8 m. Therefore, we can use the cosine function to find the length of AB.
cos(80°) = adjacent / hypotenuse
Now, we can substitute the values into the equation:
cos(80°) = AB / 8
To solve for AB, we isolate it by multiplying both sides of the equation by 8:
8 * cos(80°) = AB
Using a calculator, we find that cos(80°) is approximately 0.17365.
Now, we can substitute this value into the equation:
8 * 0.17365 = AB
This simplifies to:
1.3892 = AB
Rounding to the nearest hundredth, the length of AB is approximately 1.39 meters.