Question

An observation tower is 75 m high. A support wire is attached to the tower 20 m from the top. If the support wire and the ground form an angle of 46 degrees, what is the length of the support wire, to the nearest tenth? (Use trig!!)

Answer 1

To find the length of the support wire, use the sine function in trigonometry and solve for 'x' in the equation x = 75/sin(46). The length of the support wire is approximately 102.2 m.

Step-by-step explanation:

To find the length of the support wire, we can use trigonometry. Let's call the length of the support wire 'x'.

Using the right triangle formed by the tower, the support wire, and the ground, we can use the sine function to solve for 'x'. The sine of the angle (46 degrees) is equal to the side opposite the angle (75 m) divided by the hypotenuse (x m).

Therefore, we have sin(46) = 75/x. To solve for 'x', we can rewrite the equation as x = 75/sin(46). Calculating this, we get x = 102.2 m (rounded to the nearest tenth).