# 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 value of .

Q5:

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

Q6:

Find given is a triangle where and .

Q7:

Find given is a right-angled triangle at where .

Q8:

Find given is a rectangle where and .

• A
• B
• C
• D

Q9:

Find the value of .

• A
• B
• C
• D

Q10:

Find the value of given where is the smallest positive angle.

• A
• B
• C
• D

Q11:

Find the value of .

Q12:

Simplify .

Q13:

Simplify .

Q14:

Find the value of .

Q15:

Find given that is a right triangle at , where and .

• A
• B
• C
• D
• E

Q16:

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

• A , ,
• B , ,
• C , ,
• D , ,

Q17:

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

• A
• B
• C
• D

Q18:

Find the values of and giving the answer to three decimal places.

• A ,
• B ,
• C ,
• D ,

Q19:

In the triangle shown, is the side labelled adjacent to angle , opposite angle , or the hypotenuse?

• Ahypotenuse
• Copposite

Q20:

Find the length of giving the answer to two decimal places.

Q21:

Find the values of and giving the answer to three decimal places.

• A ,
• B ,
• C ,
• D ,

Q22:

is a right-angled triangle at , where , , and . Find the measure of giving the answer to the nearest second.

• A
• B
• C
• D

Q23:

Find the value of , given that is a triangle, where , , and is drawn perpendicular to intersecting at .

• A
• B
• C
• D

Q24:

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

• A175
• B625
• C168
• D600

Q25:

is a point inside a square with a side length of 48 cm, where and . Find the value of , given that .

• A6
• B42
• C
• D