Question

a crate is supported by two ropes. one rope makes an angle of 46°32 with the horizontal and has a tension of 87.8 lb on it. the other rope is horizontal. find the weight of the crate and the tension in the horizontal rope. the weight of the crate is □ pounds. (round to the nearest tenth as needed.)

Explanation:

Step1: Identify the vertical component of the tension

The tension in the angled rope is \( T = 87.8 \) lb, and the angle with the horizontal is \( \theta = 46^\circ \). The vertical component of the tension \( T_y \) balances the weight \( W \) of the crate. The formula for the vertical component is \( T_y = T \sin\theta \).

$$ T_y = 87.8 \times \sin(46^\circ) $$

Step2: Calculate the sine of the angle

First, find \( \sin(46^\circ) \approx 0.7193 \).

Step3: Compute the weight

Substitute the values into the formula:

$$ W = 87.8 \times 0.7193 \approx 63.2 $$

Answer:

\( 63.2 \)