Question

1. a horse is sighted on the other side of a canyon. find the width of the canyon? image of a horse and two right triangles with labels x, 100 ft, 10 ft, 7.5 ft options: 750, 75, 133.33, 97.5

Explanation:

Step1: Identify Similar Triangles

The two triangles (one with height \( x \) and base 100 ft, the other with height 7.5 ft and base 10 ft) are similar by AA (Angle-Angle) similarity (right angle and common angle). So, their corresponding sides are proportional.

Step2: Set Up Proportion

For similar triangles, \(\frac{x}{100}=\frac{7.5}{10}\).

Step3: Solve for \( x \)

Cross - multiply: \( 10x = 100\times7.5 \). Then \( 10x=750 \). Divide both sides by 10: \( x = \frac{750}{10}=75 \).

Answer:

75