# Worksheet: Trigonometric Ratios in Right Triangles

In this worksheet, we will practice finding and express 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 given is a right-angled triangle at where and .

• A, ,
• B, ,
• C, ,
• D, ,

Q2:

is a diameter of a circle with radius 62.5 cm. Point is on the circumference of the circle where and . Find the exact values of and . • A and
• B and
• C and
• D and

Q3:

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

• A, and
• B, and
• C, and
• D, and

Q4:

Find the main trigonometric ratios of given is a right-angled triangle at where the ratio between and is .

• A, ,
• B, ,
• C, ,
• D, ,

Q5:

Find given that is a right-angled triangle at where and . • A
• B
• C
• D

Q6:

In the triangle shown, is the side labeled adjacent to angle , opposite angle , or the hypotenuse? • BHypotenuse
• COpposite

Q7:

In the triangle shown, would we call the side labeled the hypotenuse, the adjacent side to angle , or the side opposite angle ? • AThe adjacent side to angle
• BThe side opposite angle
• CThe hypotenuse

Q8:

In the figure, which of the following words describes the position of the side labeled with respect to the angle ? • AOpposite
• CHypotenuse

Q9:

Find the value of given is a right-angled triangle at where and .

• A
• B
• C
• D

Q10:

is an isosceles triangle where and . Find the value of given lies on the midpoint of where .

• A
• B
• C
• D

Q11:

Find , given that is an isosceles trapezoid, where , , , and . Q12:

Find the value of , given that , , , and . • A
• B
• C
• D

Q13:

Find the value of . • A
• B
• C
• D

Q14:

What is the value of in the given triangle? • A
• B
• C
• D
• E

Q15:

Find and given is a right-angled triangle at where .

• A and
• B and
• C and
• D and

Q16:

What is the value of in the given triangle? • A
• B
• C
• D
• E

Q17:

What is the value of in the given triangle? • A
• B2
• C1
• D
• E

Q18:

is an isosceles triangle where and . Find the value of given that is the midpoint of .

• A
• B
• C
• D

Q19:

Find , given is a right-angled triangle at where and . • A
• B
• C
• D

Q20:

What is the value of in the given triangle? • A
• B
• C
• D
• E

Q21:

Find the value of given is a right triangle at where and .

• A
• B
• C
• D

Q22:

Find , given is a right-angled triangle at where and . • A
• B
• C
• D

Q23:

Find the value of given is a right-angled triangle at where .

• A
• B
• C
• D2

Q24:

What is the value of in the given triangle? • A
• B
• C
• D
• E

Q25:

is a triangle, where the ratio between its lengths , , and is . Find .

• A
• B
• C
• D