Textbook Question
Solve each right triangle. In Exercise 46, give angles to the nearest minute. In Exercises 47 and 48, label the triangle ABC as in Exercises 45 and 46. A = 39.72°, b = 38.97 m
513
views
2. Trigonometric Functions on Right Triangles
Solving Right Triangles
Multiple Choice
In right triangle , if is units and is units, what is the length of line segment ?
A
units
B
units
C
units
D
units
Verified step by step guidance1
Identify the right triangle and label the sides: given triangle \( xyz \) is right-angled, with sides \( xy = 4 \) units and \( yz = 4 \) units.
Recognize that the side \( xz \) is the hypotenuse of the right triangle since it is opposite the right angle.
Apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides:
\[ xz^2 = xy^2 + yz^2 \]
Substitute the known side lengths into the equation:
\[ xz^2 = 4^2 + 4^2 \]
Simplify the right side and then take the square root to find \( xz \):
\[ xz = \sqrt{4^2 + 4^2} = \sqrt{16 + 16} = \sqrt{32} \]
Related Videos
Related Practice
