A totem pole is being stabilized by attaching a rope at the top and anchoring it in the ground 20.4 m away from the base.The angle of elevation is 46.20. How long a rope is needed?(Answer to ONE decimal place and put only the number with no units in the answer box.)

To solve this problem, we can use the tangent of the angle of elevation, which is the opposite side (the height of the totem pole) divided by the adjacent side (the distance from the base of the pole to the anchor point). However, we want to find the length of the rope, which is the hypotenuse of the right triangle formed by the pole, the ground, and the rope. So, we should use the sine of the angle of elevation, which is the opposite side (the height of the totem pole) divided by the hypotenuse (the length of the rope).

We can rearrange the formula to solve for the length of the rope:

Length of rope = Height of totem pole / sin(angle of elevation)

We know the angle of elevation is 46.2 degrees, but we don't know the height of the totem pole. We can find it using the tangent of the angle of elevation:

Height of totem pole = tan(angle of elevation) * Distance from base to anchor

= tan(46.2) * 20.4

Once we find the height of the totem pole, we can substitute it into the first formula to find the length of the rope.

Let's calculate:

Height of totem pole = tan(46.2) * 20.4 = 19.6 m (approximately)

Length of rope = 19.6 / sin(46.2) = 26.3 m (approximately)

So, the length of the rope needed is approximately 26.3 m.