Question

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.

Answer 1

Given:

In triangle ABC, $\angle A=90^\circ, AB=1\text{ units}, AC=8\text{ units}$.

To find:

The length of BC.

Solution:

Pythagoras Theorem : In a right angled triangle,

$Hypotenuse^2=Base^2+Perpendicular^2$

In triangle ABC, angle A is right angle, so BC is hypotenuse.

Using Pythagoras theorem, we get

$BC^2=AC^2+AB^2$

$BC^2=(8)^2+(1)^2$

$BC^2=64+1$

$BC^2=65$

Taking square root on both sides.

$BC=\pm\sqrt{65}$

But side cannot be negative, so $BC=\sqrt{65}$.

Therefore, the length of BC is $\sqrt{65}\text{ units}.$

Answer 2

Using the Pythagorean Theorem, the length of BC is: 8.1 units.

Recall:

Pythagorean Theorem holds true when solving a right triangle that has side c as hypotenuse and side a and b as the other legs, thus: c² = a² + b².

Triangle ABC is shown in the diagram below, where:

• m∠A = 90°
• AB = 1 unit = a
• AC = 8 units = b
• BC = ? = c (hypotenuse)

Applying the Pythagorean Theorem, the length of BC is solved as follows:

BC = √(1² + 8²)

BC = 8.1 units

Learn more about the Pythagorean Theorem on:

https://brainly.com/question/16176867