# 11.4.1. The Sine Rule

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

- A61.7 cm
- B173 cm
- C123.5cm
- D34.6 cm

Solve the triangle , if possible, where , cm, and cm.

- AThe triangle doesn't exist.
- Bcm, , and .
- Ccm, , and .

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, ,

Determine whether the triangle has one solution, two, or no solutions, given that , cm, and cm.

- Ano solutions
- Bone solution
- Ctwo solutions

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, ,

is a trapezoid, where , cm, , , and . Find the lengths of and to the nearest centimeter.

- Acm, cm
- Bcm, cm
- Ccm, cm
- Dcm, cm

In a quadrilateral , cm, , , , and . Find the lengths of and to the nearest centimeter.

- Acm, cm
- Bcm, cm
- Ccm, cm
- Dcm, cm

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

Show Solutionis a triangle in which and cm. Determine the radius of the circumcircle in centimeters.

- A
- B
- C486
- D972

Given that is a triangle, where cm and , determine the diameter of its circumcircle.

- A cm
- B cm
- C cm
- D cm

The radius of the circumcircle of a triangle , in which , is cm. Find .

- Acm
- Bcm
- Ccm
- Dcm

Solve the triangle below approximating the side lengths to the nearest 3 decimal places.

- Acm, cm,
- Bcm, cm,
- Ccm, cm,
- Dcm, cm,

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

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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