Question

26. Find AB. Round to the nearest tenth.

Answer 1

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Answer 2

Rounded to the nearest tenth, the value of
`\( AB \approx 10.4 \)`.

To find side AB in triangle ABC, you can use the law of sines. The formula is:


`\[ (a)/(\sin A) = (b)/(\sin B) = (c)/(\sin C) \]`

In this case, let
`\( a = BC \), \( b = AC \),` and
`\( c = AB \).` You know
`\( AC = 12 \), \( \angle C = 62^\circ \), and \( \angle B = 50^\circ \).`


`\[ (12)/(\sin 62^\circ) = (AB)/(\sin 50^\circ) \]`

Now, solve for AB:


`\[ AB = (12 \cdot \sin 50^\circ)/(\sin 62^\circ) \]`

Calculate this expression to find the length of side AB, and round to the nearest tenth.

`\[ AB = (12 \cdot \sin 50^\circ)/(\sin 62^\circ) \]`

Using a calculator:


`\[ AB \approx (12 \cdot 0.766)/(0.882) \]\[ AB \approx (9.192)/(0.882) \]\[ AB \approx 10.41 \]\\`

Rounded to the nearest tenth,
`\( AB \approx 10.4 \)`.