# Worksheet: The Tangent Ratio

In this worksheet, we will practice finding an angle in a right triangle using the tangent ratio.

Q1:

Find the values of and giving your answer to the nearest second. • A,
• B,
• C,
• D,

Q2:

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

• A
• B
• C
• D

Q3:

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

• A
• B
• C
• D

Q4:

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

Q5:

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

• A
• B
• C
• D

Q6:

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

Q7:

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

Q8:

Find the value of , given is an equilateral triangle, where point lies on , , , and . • A
• B
• C
• D

Q9:

Find to two decimal places. Q10:

In the given figure, and . What is? • A
• B
• C
• D
• E

Q11:

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

Q12:

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

Q13:

Find the exact value of . • A
• B
• C
• D

Q14:

The dimensions of a rectangular yard is 13 meters by 12 meters. Triangle represents the lawn where . Find the measure of giving the answer to the nearest second. • A
• B
• C
• D

Q15:

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

Q16:

Find the length of given is a quadrilateral where and . • A cm
• B cm
• C10 cm
• D cm

Q17:

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

Q18:

In the given figure, where . What is ? • A
• B
• C
• D
• E

Q19:

Find the value of given is a square where points and lie on , , , and . • A
• B
• C
• D

Q20:

is a right-angled 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. Q21:

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

• A
• B
• C
• D

Q22:

is a triangle where and . Find the value of without using a calculator.

• A
• B21
• C
• D

Q23:

In the given figure, the two triangles are similar. Work out the value of for . Give your answer as a fraction in its simplest form.

• A
• B
• C
• D
• E

Work out the value of for . Give your answer as a fraction in its simplest form.

• A
• B
• C
• D
• E

What can be said about the value of for two similar triangles?

• AThey will never be equal.
• BThey are always equal.
• CThey are often equal.

Q24:

is a diametre of a circle with radius 17 cm. Point is on the circumference of the circle where and . Find the exact values of and . • A,
• B,
• C,
• D,

Q25:

Find the value of , given is a right-angled triangle at where and giving the answer to two decimal places.