In the given diagram:
measure angle DAB + measure angle BAC = 90 degrees
we are given that measure angle DAB = 10 degrees
Therefore:
measure angle BAC = 90 - 10 = 80 degrees
Now, triangle ABC is a right-angled triangle which means that we can use the trigonometric functions.
The function that we will use is:
cos theta = (adjacent) / (hypotenuse) where
theta = 80 degrees
adjacent = 500
hypotenuse is "x" that we want to calculate.
Substitute to get x as follows:
cos 80 = 500 / x
x = 500 / cos 80 = 500 / 0.1736 = 2879.4 m
