Worksheet: The Tangent Ratio
In this worksheet, we will practice finding an angle in a right triangle using the tangent ratio.
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-angled 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
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-angled 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 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
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 centimetre, 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.