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kudzordzifrancis
ANSWER

[tex]|BC|=12\sqrt{2}\: ft[/tex]

EXPLANATION

The given right triangle is an isosceles triangle because

[tex]m \: < \: B = 45 \degree = m \: < \: C[/tex]
This implies that,

[tex]|AB|=12ft=|AC|[/tex]

From the Pythagoras Theorem,

[tex]|BC|^2=|AB|^2+|AC|^2[/tex]

[tex]|BC|^2= {12}^{2} + {12}^{2} [/tex]

[tex]|BC|^2=2 \times {12}^{2} [/tex]

[tex]|BC| = \sqrt{ {12}^{2} \times 2 } [/tex]

[tex]|BC|=12\sqrt{2}\: ft[/tex]
alinakincsem

Answer:

[tex]BC = 12\sqrt{2}[/tex]

Step-by-step explanation:

We are given a right angled triangle ABC with the side AC 12 feet long while the measure of the angle B is 45 degrees.

We are to find the length of the side BC. For that, we can use the sine function:

[tex] sin 45 = \frac {12} {BC} [/tex]

Since sin 45 is equal to [tex]\frac{1}{\sqrt{2} }[/tex] so we can substitute this value instead to get the answer in simple radical form.

[tex] \frac{1}{\sqrt{2} } = \frac {12} {BC} [/tex]

[tex]BC = \frac{12}{\frac{1}{\sqrt{2} }}[/tex]

[tex]BC = 12\sqrt{2}[/tex]

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