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Use sine, cosine and tangent to ﬁnd missing angles 4 Alex is calculating the size of angle x. Here are her calculations. a) Alex has made two mistakes. Explain each mistake. Mistake 1 Mistake 2 b) Find the size of angle x to the nearest degree. x = c) How could Alex have noticed her answer was incorrect when checking her solutions? Discuss it with a partner. 5 a) Work out the size of the angle marked y. Give your answer to 1 decimal place. y = ° b) Ron says, “To ﬁnd the other angle, I’d need to use trigonometry again.” Do you agree? Discuss it with a partner. © White Rose Maths 2020 1 Complete the calculations. a) sin 30° = 0.5 c) tan 45° = 1 sin –1 0.5 = ° tan –1 1 = ° b) cos 60° = 0.5 d) sin 90° = 1 cos –1 0.5 = ° sin –1 1 = ° 2 Which calculation would work out the value of Ѳ? Tick your answers. a) sin Ѳ = 0.8 sin 0.8 cos 0.8 tan 0.8 sin -1 0.8 cos -1 0.8 tan -1 0.8 b) cos Ѳ = 0.45 sin 0.45 cos 0.45 tan 0.45 sin -1 0.45 cos -1 0.45 tan -1 0.45 c) tan Ѳ = 1.4 sin 1.4 cos 1.4 tan 1.4 sin -1 1.4 cos -1 1.4 tan -1 1.4 3 Use your calculator to ﬁnd the value of Ѳ to the nearest degree. a) sin Ѳ = 0.2 c) tan Ѳ = 1.7 e) tan Ѳ = 8 5 Ѳ = ° Ѳ = ° Ѳ = ° b) cos Ѳ = 0.15 d) sin Ѳ = 0.6 f) cos Ѳ = 2 7 Ѳ = ° Ѳ = ° Ѳ = ° 6 cm x 8 cm tan x = 6 8 x = tan 6 8 x = 0.01° 17 cm y 7 cm

# Use sine, cosine and tangent to find 4 missing angles...Use sine, cosine and tangent to find missing angles 4 Alex is calculating the size of angle x. Here are her calculations. a)

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### Text of Use sine, cosine and tangent to find 4 missing angles...Use sine, cosine and tangent to find missing... Use sine, cosine and tangent to find missing angles

4 Alex is calculating the size of angle x.

Here are her calculations.

a) Alex has made two mistakes. Explain each mistake.

Mistake 1

Mistake 2

b) Find the size of angle x to the nearest degree.

x =

c) How could Alex have noticed her answer was incorrect when checking

her solutions? Discuss it with a partner.

5 a) Work out the size of the angle marked y.

y = °

b) Ron says, “To find the other angle, I’d need to use trigonometry again.”

Do you agree?

Discuss it with a partner.© White Rose Maths 2020

1 Complete the calculations.

a) sin 30° = 0.5 c) tan 45° = 1

sin–1 0.5 = ° tan–1 1 = °

b) cos 60° = 0.5 d) sin 90° = 1

cos–1 0.5 = ° sin–1 1 = °

2 Which calculation would work out the value of Ѳ? Tick your answers.

a) sin Ѳ = 0.8

sin 0.8

cos 0.8

tan 0.8

sin-1 0.8

cos-1 0.8

tan-1 0.8

b) cos Ѳ = 0.45

sin 0.45

cos 0.45

tan 0.45

sin-1 0.45

cos-1 0.45

tan-1 0.45

c) tan Ѳ = 1.4

sin 1.4

cos 1.4

tan 1.4

sin-1 1.4

cos-1 1.4

tan-1 1.4

3 Use your calculator to find the value of Ѳ to the nearest degree.

a) sin Ѳ = 0.2 c) tan Ѳ = 1.7 e) tan Ѳ = 85

Ѳ = ° Ѳ = ° Ѳ = °

b) cos Ѳ = 0.15 d) sin Ѳ = 0.6 f) cos Ѳ = 27

Ѳ = ° Ѳ = ° Ѳ = °

6 cm

x

8 cm

tan x = 68

x = tan 68

x = 0.01°

17 cm

y

7 cm 7 A ship sets sail north from point O.

It sails for 45 km then turns due east and sails for 35 km to point P.

a) Draw a sketch of the right-angled triangle formed by the path that the

ship takes, and the line segment OP.

b) What is the bearing of point P from point O?

8 Work out the size of angle ADC.

6 Find the size of angle Ѳ in each triangle.

a) d)

Ѳ = ° Ѳ = °

b) e)

Ѳ = ° Ѳ = °

c) f)

Ѳ = ° Ѳ = °

12 cm

Ѳ

5 cm

4 cm

Ѳ

7 cm

18.3 mѲ

12.1 m

9.2 m

Ѳ

8.7 m

5.7 mm

Ѳ

2.4 mm

6.4 cm

Ѳ

9.3 cmBC

24 cm

31 cmA

D

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