# Worksheet: The Tangent Ratio

Q1:

Find the value of , given is an equilateral triangle, where point lies on , , , and .

• A
• B
• C
• D

Q2:

Find to two decimal places.

Q3:

In the given figure, and . What is?

• A
• B
• C
• D
• E

Q4:

is a right triangle at , where . Point lies on and point lies on where . Find the length of given and . Give the answer to two decimal places.

• A 33.94 cm
• B 84.58 cm
• C 174.67 cm
• D 9.94 cm
• E 29.24 cm

Q5:

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

• A
• B
• C
• D

Q6:

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

• A
• B
• C
• D

Q7:

is a right triangle at where and . Find the length of giving the answer to two decimal places.

• A 8.19 cm
• B 5.74 cm
• C 19.28 cm
• D 14.28 cm

Q8:

Find the exact value of .

• A
• B
• C
• D

Q9:

is a right triangle at where and . Find the length of giving the answer to two decimal places.

• A 23.49 cm
• B 32.32 cm
• C 11.17 cm
• D 13.80 cm
• E 26.15 cm

Q10:

is a right triangle at where and . Find the length of giving the answer to two decimal places.

• A 14.59 cm
• B 28.63 cm
• C 5.90 cm
• D 6.62 cm
• E 25.51 cm

Q11:

The dimensions of a rectangular garden is 13 metres by 12 metres. Triangle represents the lawn where . Find the measure of giving the answer to the nearest second.

• A
• B
• C
• D

Q12:

is a triangle where lies on such that , and . Find the area of giving the answer to two decimal places.

Q13:

is a rhombus where and . Find giving the answer to the nearest second.

• A
• B
• C
• D

Q14:

Find the length of given is a quadrilateral where and .

• A cm
• B cm
• C 10 cm
• D cm

Q15:

is a triangle where , , , and . Find, to the nearest centimeter, the length of .

• A 45 cm
• B 33 cm
• C 46 cm
• D 31 cm
• E 23 cm

Q16:

In the given figure, where . What is ?

• A
• B
• C
• D
• E

Q17:

Find the value of given is a square where points and lie on , , , and .

• A
• B
• C
• D

Q18:

is a right triangle at . Point lies on and point lies on where . Find the area of the trapezoid given , , and . Give the answer to two decimal places.

• A
1β890.00
cm2
• B 74.06 cm2
• C 481.89 cm2
• D 630.00 cm2

Q19:

Find the values of and giving your answer to the nearest second.

• A ,
• B ,
• C ,
• D ,

Q20:

Find the values of and giving your answer to the nearest second.

• A ,
• B ,
• C ,
• D ,

Q21:

is a triangle where , , , and . Find giving the answer to the nearest second.

• A
• B
• C
• D

Q22:

The following figure represents a line segment joining two points and . Find the measure of the angle included between and the -axis giving the answer to the nearest second.

• A
• B
• C
• D

Q23:

The following figure represents a line segment joining two points and . Find the measure of the angle included between and the -axis giving the answer to the nearest second.

• A
• B
• C
• D

Q24:

A flagpole 5.9 meters tall casts a 2.8-meter shadow. Find the angle of inclination of the sun giving the answer to the nearest minute.

• A
• B
• C
• D

Q25:

A flagpole 5.9 meters tall casts a 2.8-meter shadow. Find the angle of inclination of the sun giving the answer to the nearest minute.

• A
• B
• C
• D