Round answer to two significant digits.
A telephone pole 40 feet high is situated on an 13° (H) slope from the horizontal. The measure of angle CAB is 21°. Find the length of the guy wire AC.
To find the length of the guy wire AC, we can use trigonometry. First, let's define the given information:
Height of telephone pole (opposite side of angle CAB) = 40 feet
Angle of slope (angle H) = 13°
Measure of angle CAB = 21°
Now, let's break down the problem and use trigonometric ratios. Since we know the height of the pole and the angle CAB, we can use the tangent ratio:
Tangent of angle CAB = Opposite / Adjacent
In this case, the opposite side is the height of the pole and the adjacent side is the length of the guy wire AC. So, we can write the equation as:
tan(21°) = 40 / AC
To find AC, we rearrange the equation:
AC = 40 / tan(21°)
Using a calculator, we can evaluate the tangent of 21° and then substitute it back into the equation:
AC = 40 / 0.3855
AC ≈ 103.710 feet (rounded to six decimal places)
Since the question asks for the answer to be rounded to two significant digits, we can write the final answer as:
AC ≈ 100 feet