Question

Find the length of segment BC.
A) 2n
B) √n
C) √2n
D) $\frac{n\sqrt{2} }{2}$
E) n√2

Answer 1

Answer:

D

Step-by-step explanation:

Since the triangle is right using the cosine ratio to solve for BC

noting that the exact value of cos45° = $\frac{1}{\sqrt{2} }$, so

cos45° = $\frac{BC}{AC}$ = $\frac{BC}{n}$

Multiply both sides by n

n × cos45° = BC

n × $\frac{1}{\sqrt{2} }$ = BC

$\frac{n}{\sqrt{2} }$ × $\frac{\sqrt{2} }{\sqrt{2} }$ = BC

Hence BC = $\frac{n\sqrt{2} }{2}$ → D

Answer 2

The right-angle triangle is given with one angle of 45 degrees. The length of segment BC is n√2/2.

What is the right triangle?

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.

The angle of a right angle is always 90 degrees.

Since the triangle is right angle

by using the cosine ratio to solve for BC

The value of cos45° = 1/√2 ,

So,

cos45° = BC / AC = BC / n

Multiply both sides by n

n × cos45° = BC

n × 1/√2 = BC

n/√2 × √2 /√2 = BC

Hence, BC = n√2/2

Learn more about a right angle;

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