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.
No idea where A , B , or C are
To find the length of the guy wire AC, we can use trigonometry. Let's break down the problem step by step.
Step 1: Draw a diagram.
Draw a diagram of the situation described in the problem. Make sure to label all the given information. Here's a simple representation:
C
/ \
/ \
/ \
A-------------B
Step 2: Identify the right triangle.
In our diagram, triangle ABC is a right triangle because pole AB is perpendicular to the ground. Hence, angle CAB is a right angle.
Step 3: Determine the side lengths.
We know that AB, the height of the pole, is 40 feet. We need to find the length of side AC, the guy wire.
Step 4: Use trigonometry.
Since we have a right triangle, we can use the trigonometric ratio involving the angle 13°.
In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the hypotenuse (the longest side).
In our case, sin(13°) = opposite side / hypotenuse.
Let's use this formula and solve for the opposite side, which is AC (the guy wire):
sin(13°) = AC / 40
Step 5: Solve for AC.
To solve for AC, we need to isolate it in the equation. Multiply both sides of the equation by 40:
40 * sin(13°) = AC
By evaluating sin(13°) using a calculator, we find that sin(13°) is approximately 0.224951.
Therefore, AC is approximately:
AC = 40 * 0.224951
AC ≈ 8.99804
The length of the guy wire AC is approximately 8.99804 feet.