Question

x-tracredit extended practice please show your work! dbwb 1. find the missing side in each triangle. round to the nearest hundredth, if needed. a. triangle with legs 8 in. and 6 in. b. triangle with legs 4 in. and 7 in. c. triangle with base 7 ft and hypotenuse 25 ft d. triangle with leg 8 m and hypotenuse 16 m 2. one leg of an isosceles right triangle has length 50 feet. a. write an equation that you could use to find the length of the triangle’s hypotenuse. b. find the length of the hypotenuse. round your answer to the nearest tenth of a foot. 3. a right triangle has base 5 inches and height 12 inches. how long is its hypotenuse? 4. a right triangle has one leg with length 20 feet and hypotenuse length 29 feet. how long is the other leg? 5. can a right triangle be formed with side lengths 30 inches, 40 inches, and 50 inches?

Explanation:

Problem 1a:

Step1: Identify triangle type (right triangle)

The triangle has legs 6 in and 8 in, so it's a right triangle. Use Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \)

Step2: Substitute values

\( a = 6 \), \( b = 8 \), so \( c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \)

Step1: Right triangle, legs 4 in and 7 in

Use Pythagorean theorem: \( c = \sqrt{a^2 + b^2} \)

Step2: Substitute values

\( a = 4 \), \( b = 7 \), so \( c = \sqrt{4^2 + 7^2} = \sqrt{16 + 49} = \sqrt{65} \approx 8.06 \)

Step1: Right triangle, leg 7 ft, hypotenuse 25 ft

Use Pythagorean theorem: \( b = \sqrt{c^2 - a^2} \)

Step2: Substitute values

\( a = 7 \), \( c = 25 \), so \( b = \sqrt{25^2 - 7^2} = \sqrt{625 - 49} = \sqrt{576} = 24 \)

Answer:

10 inches

Problem 1b: