Question

calculator note: image is not drawn to scale. hays is standing outside on a sunny day. he is 6 ft tall and casts a 4 ft shadow. what is the distance from the top of hayss head to the end of his shadow? round to the nearest tenth, if necessary. 4.5 ft 5 ft 7.2 ft 10 ft

Explanation:

Step1: Identify the triangle type

This is a right triangle problem where the height (Hays's height) is 6 ft, the base (shadow length) is 4 ft, and we need to find the hypotenuse (distance from head to shadow end).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \( c = \sqrt{a^2 + b^2} \), where \( a = 6 \), \( b = 4 \).
So, \( c = \sqrt{6^2 + 4^2} = \sqrt{36 + 16} = \sqrt{52} \).

Step3: Calculate the value

\( \sqrt{52} \approx 7.211 \), which rounds to 7.2.

Answer:

7.2 ft (corresponding to the option "7.2 ft")