Question

determine the value of x in each of the right triangles. write your final answer in sim decimal rounded to the nearest tenth. 1. right triangle with legs x and 12, hypotenuse 15 2. right triangle with legs 9 and 11, hypotenuse x 3. partially visible right triangle

Explanation:

For Problem 1:

Step1: Apply Pythagorean theorem

In a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is hypotenuse, \( a,b \) are legs. Here, hypotenuse \( c = 15 \), one leg \( b = 12 \), find \( x=a \). So \( x^2 + 12^2 = 15^2 \).

Step2: Solve for \( x \)

\( x^2 = 15^2 - 12^2 = 225 - 144 = 81 \), then \( x = \sqrt{81}=9 \).

For Problem 2:

Step1: Apply Pythagorean theorem

Hypotenuse \( x \), legs \( a = 9 \), \( b = 11 \). So \( 9^2 + 11^2 = x^2 \).

Step2: Calculate \( x \)

\( x^2 = 81 + 121 = 202 \), \( x=\sqrt{202}\approx14.2 \) (rounded to nearest tenth).

Answer:

1. \( x = 9 \)
2. \( x \approx 14.2 \)