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In this lesson, we will learn how to solve triangles using the sine law, the cosine law, or both of them.

Q1:

π΄ π΅ πΆ π· is a parallelogram where π is the point of intersection to the diagonals, π΄ πΆ = 2 1 . 1 c m , π β π΄ π π· = 8 0 5 4 β² β and π β πΆ π΄ π΅ = 5 3 5 4 β² β . Find the area of the parallelogram giving the answer to two decimal places.

Q2:

π΄ π΅ πΆ is a triangle, where π· is the midpoint of π΅ πΆ , π β π΅ = 2 8 β , π β π΄ = 6 9 β , and π = 2 0 c m . Find the length of π΄ π· giving the answer to two decimal places.

Q3:

π΄ π΅ πΆ π· is a quadrilateral where π β π΄ π΅ πΆ = 9 0 β , π β π΅ π΄ π· = 4 1 β , π΄ π΅ = π΄ π· = 3 0 . 9 c m and π΅ π· = π΅ πΆ . Find the area of π΄ π΅ πΆ π· giving the answer to two decimal places.

Q4:

π΄ π΅ πΆ is a right-angled triangle at π΅ where π΄ π΅ = 4 4 c m and π΅ πΆ = 6 8 c m . Find the length of π΄ πΆ to two decimal places and then the measure of angles π΄ and πΆ to the nearest second.

Q5:

In a parallelogram π΄ π΅ πΆ π· , π΅ πΆ = 8 i n c h e s and π΄ π΅ = 5 i n c h e s , where π β π΄ π΅ πΆ = 1 3 4 β . Work out the length of π΄ πΆ . Give your answer to 2 decimal places.

Q6:

Find the area of π΄ π΅ πΆ π· given πΈ is the point of intersection of π΄ πΆ and π΅ π· , π΄ πΈ = 5 c m , πΈ πΆ = 8 . 9 c m , πΈ π· = 7 . 7 c m , and π β π΄ πΈ π΅ = 8 0 β . Give the answer to the nearest square centimetre.

Q7:

π΄ π΅ πΆ is a right-angled triangle at π΅ where π β πΆ = 6 2 β and π΄ πΆ = 1 7 c m . Find the lengths of π΄ π΅ and π΅ πΆ giving the answer to two decimal places and the measure of β π΄ giving the answer to the nearest degree.

Q8:

π΄ π΅ πΆ is a right-angled triangle at π΅ where π΄ π΅ = 2 7 c m and π β π΄ = 6 3 β . Find the lengths π΄ πΆ and π΅ πΆ giving the answer to two decimal places and the measure of angle πΆ giving the answer to the nearest degree.

Q9:

π΄ π΅ πΆ is a right-angled triangle at π΅ where π β πΆ = 1 . 1 8 8 r a d and π΄ πΆ = 1 2 c m . Find π β π΄ in radians and lengths π΄ π΅ and π΅ πΆ giving all answers to three decimal places.

Q10:

The side length of a regular pentagon π΄ π΅ πΆ π· πΈ is 25.81 cm. Find the length of the diagonal π΄ πΆ giving the answer to two decimal places.

Q11:

π΄ π΅ πΆ is a triangle where π β π΄ = 3 0 β , the ratio between π and π is β 3 βΆ 2 and the area of the circumcircle is 2 2 5 π cm^{2}. Find the perimeter of the triangle π΄ π΅ πΆ giving the answer to the nearest centimetre.

Q12:

is a trapezium, where , , , , and . Find the lengths of and giving the answer to the nearest centimetre.

Q13:

π΄ π΅ πΆ is a triangle where π΄ π΅ = 7 c m , π β π΅ = 6 0 β and the area of the triangle is 9 1 β 3 cm^{2}. Find the perimeter of π΄ π΅ πΆ giving the answer to two decimal places.

Q14:

π΄ π΅ πΆ is a right-angled triangle at π΅ where π β π΄ = 0 . 9 4 2 r a d and π΄ π΅ = 1 9 c m . Find π β πΆ in radians and the lengths π΅ πΆ and π΄ πΆ giving all answers to three decimal places.

Q15:

π΄ π΅ πΆ is a triangle where π = 2 6 cm, π = 2 2 cm and π = 6 cm. Find the radius of the circumcircle giving the answer to three decimal places.

Q16:

π΄ π΅ πΆ is a triangle where π = 4 4 c m , π = 3 1 c m and π β πΆ = 6 9 β . Point π· lies on π΄ π΅ such that πΆ π· β π΄ π· . Find the length of πΆ π· giving the answer to two decimal places.

Q17:

π΄ π΅ πΆ π· is a trapezium where π΄ π· β₯ π΅ πΆ , π΅ πΆ = 2 0 c m , π β π΄ π΅ πΆ = 6 1 β , π΄ π· = 1 1 c m and π β π΅ π΄ πΆ = 5 9 β . Find the area of the trapezium giving the answer to the nearest square centimetre.

Q18:

π΄ π΅ πΆ is a triangle, where π = 1 9 cm, π = 9 cm, and π β πΆ = 4 5 β . Find the radius of the circumcircle giving the answer to two decimal places.

Q19:

π΄ π΅ πΆ π· is a trapezium, where π΄ π· β₯ π΅ πΆ , π΄ π· = 2 0 c m , π β π΅ = 5 5 β , π β π· = 8 0 β , and π β π΄ πΆ π΅ = 5 2 β . Find the area of the trapezium giving the answer to the nearest square centimetre.

Q20:

π΄ π΅ πΆ is a triangle where s i n s i n s i n π΄ 2 5 = π΅ 2 9 = πΆ 1 5 . Find the largest angle in π΄ π΅ πΆ giving the answer to the nearest degree.

Q21:

π΄ π΅ πΆ π· is a quadrilateral where π΄ π΅ = 1 6 c m , π β π΄ π· π΅ = 4 0 β , π β π· π΅ π΄ = 1 0 0 β , π΅ πΆ = 2 1 c m and π· πΆ = 9 c m . Find π β π΅ πΆ π· giving the answer to the nearest second and the area of π΅ πΆ π· giving the answer to three decimal places.

Q22:

π΄ π΅ πΆ π· is a quadrilateral where π΄ π΅ = 1 4 c m , π β π΄ π· π΅ = 7 0 β , π β π· π΅ π΄ = 4 0 β , π΅ πΆ = 2 6 c m and π· πΆ = 2 7 c m . Find π β π΅ πΆ π· giving the answer to the nearest second and the area of π΅ πΆ π· giving the answer to three decimal places.

Q23:

π΄ π΅ πΆ π· is a quadrilateral where π΄ π΅ = 7 c m , π β π΄ π· π΅ = 6 1 β , π β π· π΅ π΄ = 5 8 β , π΅ πΆ = 2 4 c m and π· πΆ = 1 9 c m . Find π β π΅ πΆ π· giving the answer to the nearest second and the area of π΅ πΆ π· giving the answer to three decimal places.

Q24:

π΄ π΅ πΆ is an isosceles triangle where π΄ π΅ = π΄ πΆ = 4 7 c m and π΅ πΆ = 1 0 c m . Find the angles in the triangle giving the answer to the nearest second.

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