Question

1. 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 triangles hypotenuse.
b. find the length of the hypotenuse. round your answer to the nearest tenth of a foot.

1. a right triangle has base 5 inches and height 12 inches. how long is its hypotenuse?
2. a right triangle has one leg with length 20 feet and hypotenuse length 29 feet. how long is the other le
3. can a right triangle be formed with side lengths 30 inches, 40 inches, and 50 inches?

Explanation:

Question 2a

Step1: Recall Pythagorean theorem

For a right triangle, \( a^2 + b^2 = c^2 \), where \( a,b \) are legs, \( c \) is hypotenuse. In isosceles right triangle, \( a = b = 50 \) ft.

Step2: Substitute values into theorem

Substitute \( a = 50 \), \( b = 50 \) into \( a^2 + b^2 = c^2 \), get \( 50^2 + 50^2 = c^2 \).

Step1: Calculate left - hand side of equation

From 2a, \( 50^2+50^2 = 2500 + 2500=5000 \), so \( c^2 = 5000 \).

Step2: Solve for \( c \)

Take square root: \( c=\sqrt{5000}\approx70.7 \) (rounded to nearest tenth).

Step1: Apply Pythagorean theorem

Let \( a = 5 \) inches, \( b = 12 \) inches, then \( c^2=a^2 + b^2 \).

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

\( 5^2+12^2 = 25 + 144 = 169 \).

Step3: Find \( c \)

\( c=\sqrt{169}=13 \) inches.

Answer:

\( 50^2 + 50^2 = c^2 \) (where \( c \) is the hypotenuse length)

Question 2b