The following diagram shows a triangle ABS, where BC=5, B^=60∘, C^=40∘. Calculate AB to the nearest whole number.

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The following diagram shows a triangle ABS, where BC=5, B^=60∘, C^=40∘. Calculate AB to the nearest whole number.

Lupe Kirkland · Accepted Answer

Step 1&amp;nbsp;The relationship between the sides and angles of non-right (oblique) triangles is known as the Law of Sines.Simply, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.&amp;nbsp;Step 2&amp;nbsp;Using hte law of sine in&amp;nbsp;△ABC&amp;nbsp;⇒ACsin⁡B=ABsin⁡C&amp;nbsp;⇒5sin⁡60∘=xsin⁡40∘&amp;nbsp;⇒sin⁡40∘=0.643&amp;nbsp;and&amp;nbsp;sin⁡60∘=0.866&amp;nbsp;⇒x=5×sin⁡40∘sin⁡60∘=5×0.6430.866=3.71cm&amp;nbsp;⇒x=4cm&amp;nbsp;(to the nearest whole number)

The following diagram shows a triangle ABS, where BC=5,\ \hat{B}=60^{\circ},\

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