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In this lesson, we will learn how to use the rule of sines to solve SSA (side-side-angle) ambiguous triangles.

Q1:

π΄ π΅ πΆ is a triangle, where π β π΅ = 1 1 0 β , π = 1 6 cm, and π = 1 2 cm. How many possible solutions are there for the other lengths and angles?

Q2:

π΄ π΅ πΆ is a triangle where π = 1 3 . 8 c m , π = 1 5 . 9 c m and π β π΄ = 2 8 β . Find all possible values for the other lengths and angles giving lengths to two decimal places and angles to the nearest second.

Q3:

is a triangle, where , , and . If the triangle exists, find all the possible values for the other lengths and angles giving the lengths to two decimal places and angles to the nearest second.

Q4:

is a triangle, where , , and . If the triangle exists, find all the possible values for the other lengths and angles in , giving the lengths to two decimal places and angles to the nearest degree.

Q5:

For the given figure, π΄ π΅ = 1 1 , π΅ πΆ = 9 , and π β π΅ π΄ πΆ = 4 1 β . Use the law of sines to work out the size of β π΄ πΆ π΅ . Give your answer to two decimal places.

Q6:

π΄ π΅ πΆ is a triangle, where π β π΄ = 7 0 β , π΅ πΆ = 3 c m , and π΄ πΆ = 3 9 c m . If the triangle exists, find all the possible values for the other lengths and angles in β³ π΄ π΅ πΆ giving the lengths to two decimal places and angles to the nearest degree.

Q7:

π΄ π΅ πΆ is a triangle where π β π΄ = 4 0 β , π = 5 c m and π = 4 c m . If the triangle exists, find all the possible values for the other lengths and angles in π΄ π΅ πΆ giving lengths to two decimal places and angles to the nearest second.

Q8:

π΄ π΅ πΆ is a triangle, where π = 2 8 c m , π = 1 7 c m , and π β πΆ = 6 0 β . Find the missing length rounded to three decimal places and the missing angles rounded to the nearest degree.

Q9:

π΄ π΅ πΆ is a triangle, where π β π΅ = 7 0 β , π = 3 cm, and π = 6 cm. How many possible solutions are there for the other lengths and angles?

Q10:

π΄ π΅ πΆ is a triangle, where π β π΅ = 1 3 0 β , π = 1 7 cm, and π = 3 cm. How many possible solutions are there for the other lengths and angles?

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