Question

3 problem 2
in triangle abc, the measure of angle a is 90°. the length of ab is 1 unit. the length of ac is 8 units. find the length of bc. round to the nearest tenth if needed.
type your answer in the box.
bc = \boxed{} units

Explanation:

Step1: Identify triangle type

Triangle \( ABC \) is right - angled at \( A \), so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - angled triangle with legs \( a \) and \( b \) and hypotenuse \( c \), \( c^{2}=a^{2}+b^{2} \). In triangle \( ABC \), \( AB \) and \( AC \) are the legs and \( BC \) is the hypotenuse. Let \( AB = 1 \) unit and \( AC=8 \) units, and \( BC = c \).

Step2: Apply Pythagorean theorem

According to the Pythagorean theorem, \( BC^{2}=AB^{2}+AC^{2} \). Substitute \( AB = 1 \) and \( AC = 8 \) into the formula:
\( BC^{2}=1^{2}+8^{2}=1 + 64=65 \)

Step3: Solve for \( BC \)

Take the square root of both sides to find \( BC \): \( BC=\sqrt{65}\approx8.1 \) (rounded to the nearest tenth)

Answer:

\( 8.1 \)