Question

find the unknown length in the right triangle. image of a right triangle with vertical leg 19 ft, horizontal leg 33 ft, hypotenuse marked ? the unknown length is approximately blank box dropdown with ft², ft, ft³ (type a whole number or decimal rounded to the thousandth as needed.) question 42, 6.6.33 hw score: 87.93%, 51 of 58 points points: 0 of 1 save

Explanation:

Step1: Identify the formula

For a right triangle, we use the Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \), where \( a = 33 \) ft, \( b = 19 \) ft, and \( c \) is the hypotenuse (unknown length).

Step2: Calculate \( a^2 + b^2 \)

\( a^2 = 33^2 = 1089 \), \( b^2 = 19^2 = 361 \). Then \( a^2 + b^2 = 1089 + 361 = 1450 \).

Step3: Find the square root

\( c = \sqrt{1450} \approx 38.079 \) (rounded to the thousandth place). Also, the unit for length is "ft".

Answer:

The unknown length is approximately \( 38.079 \) ft.