# 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.