# 11.4.1. The Sine Rule

is a triangle; , , and cm. Determine the length of in centimetres.

• A61.7 cm
• B173 cm
• C
123.5
cm
• D34.6 cm
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Solve the triangle , if possible, where , cm, and cm.

• AThe triangle doesn't exist.
• Bcm, , and .
• Ccm, , and .
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is a triangle, where , cm, and cm. Determine all the possible solutions of the triangle if it exists.

• Acm, ,
• BThe triangle does not exist.
• Ccm, ,
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Determine whether the triangle has one solution, two, or no solutions, given that , cm, and cm.

• Ano solutions
• Bone solution
• Ctwo solutions
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Given that , cm, and cm, find all the possible solutions of a triangle approximating measure of angles to the nearest second and length of sides to the nearset hundredth, if it exists.

• Acm, ,
• Bcm, ,
• Ccm, , or cm, ,
• Dcm, , or cm, ,
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is a trapezoid, where , cm, , , and . Find the lengths of and to the nearest centimeter.

• Acm, cm
• Bcm, cm
• Ccm, cm
• Dcm, cm
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In a quadrilateral , cm, , , , and . Find the lengths of and to the nearest centimeter.

• Acm, cm
• Bcm, cm
• Ccm, cm
• Dcm, cm
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Given that is an equilateral triangle of side length cm, determine the circumcircle's diameter in centimeters.

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In triangle , if , find .

• A
• B
• C
• D
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If is the radius of the circumcircle of triangle , find in terms of .

• A
• B
• C
• D
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is a triangle in which and cm. Determine the radius of the circumcircle in centimeters.

• A
• B
• C486
• D972
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Given that is a triangle, where cm and , determine the diameter of its circumcircle.

• A cm
• B cm
• C cm
• D cm
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The radius of the circumcircle of a triangle , in which , is cm. Find .

• Acm
• Bcm
• Ccm
• Dcm
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Solve the triangle below approximating the side lengths to the nearest 3 decimal places.

• Acm, cm,
• Bcm, cm,
• Ccm, cm,
• Dcm, cm,
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The figure below represents the position of three towns. If the distance between city A and city B on the map is km, the measure of the angle at city A is , and that at city C is , find the distance between A and C and the distance between B and C to the nearest kilometre.

• Akm, km
• Bkm, km
• Ckm, km
• Dkm, km
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Two boys are standing on a riverbank; the point represents the first boy's location, and the point represents the second's. If a boat is sailing in the river at the point , determine the distance between the second boy and the boat to the nearest metre.

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