In this lesson, we will learn how to find the values of the three trigonometric ratios—sine, cosine, and tangent—for a given angle in a right triangle.

Q1:

Find the main trigonometric ratios of ∠ 𝐵 given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐶 where 𝐴 𝐵 = 3 0 c m and 𝐵 𝐶 = 1 8 c m .

Q2:

Find the main trigonometric ratios of ∠ 𝐵 given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐶 where 𝐴 𝐵 = 4 0 c m and 𝐵 𝐶 = 3 2 c m .

Q3:

Find the main trigonometric ratios of ∠ 𝐵 given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐶 where 𝐴 𝐵 = 5 c m and 𝐵 𝐶 = 3 c m .

Q4:

Find the main trigonometric ratios of ∠ 𝐵 given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐶 where 𝐴 𝐵 = 3 5 c m and 𝐵 𝐶 = 2 8 c m .

Q5:

Find the main trigonometric ratios of ∠ 𝐵 given 𝐴 𝐵 𝐶 is a right-angled triangle at 𝐶 where 𝐴 𝐵 = 2 5 c m and 𝐵 𝐶 = 7 c m .

Q6:

𝐴 𝐵 is a diametre of a circle with radius 62.5 cm. Point 𝐶 is on the circumference of the circle where 𝐴 𝐶 ⊥ 𝐶 𝐵 and 𝐴 𝐶 = 7 5 c m . Find the exact values of c o s 𝐴 and s i n 𝐵 .

Q7:

𝐴 𝐵 is a diametre of a circle with radius 48.5 cm. Point 𝐶 is on the circumference of the circle where 𝐴 𝐶 ⊥ 𝐶 𝐵 and 𝐴 𝐶 = 7 2 c m . Find the exact values of c o s 𝐴 and s i n 𝐵 .

Q8:

Find the main trigonometric ratios of given is a right triangle at where .

Q9:

Q10:

Q11:

Find 𝑥 in the given figure. Give your answer to two decimal places.

Q12:

Find 𝑚 ∠ 𝐵 given 𝐴 𝐵 𝐶 is a triangle where 𝑚 ∠ 𝐴 = 1 1 1 ∘ and s i n c o s 𝐶 = 𝐶 .

Q13:

Find given is a right triangle at where .

Q14:

Find c o t 𝛼 given 𝐴 𝐵 𝐶 𝐷 is a rectangle where t a n 𝜃 = 1 0 1 7 and 𝐵 𝐹 ⟂ 𝐴 𝐸 .

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