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Lesson: The Sine Ratio

Video

12:52

Sample Question Videos

Worksheet • 25 Questions • 2 Videos

Q1:

Find the value of πœƒ giving the answer in radians to two decimal places.

Q2:

A builder leans a 5-foot plank of wood against a vertical wall. If one end of the plank is 3 feet from the bottom of the wall, what is the angle between the plank and the wall?

Q3:

The base of a truck is 2 feet off the ground and a 20-foot ramp is used to load the truck. Find, to two decimal places, the angle the ramp makes with the horizontal ground.

Q4:

In the given figure, 𝐡 𝐴 has been extended to the point 𝐷 such that 𝐡 𝐷 and 𝐷 𝐢 are perpendicular.

Work out the value of s i n 1 1 0 to 4 decimal places.

Work out the value of s i n 7 0 to 4 decimal places.

Work out the length of 𝐷 𝐢 to 2 decimal places.

Work out the area of the triangle 𝐴 𝐡 𝐢 to 2 decimal places.

Q5:

A circle has a radius of 16 cm. A chord is drawn where the central angle is 8 0 ∘ . Find the length of the chord giving the answer to three decimal places.

Q6:

In the given figure, π‘š ∠ 𝐡 𝐴 𝐢 = 9 0 ∘ and 𝐴 𝐷 βŠ₯ 𝐡 𝐢 . What is 𝐴 𝐢 πœƒ s i n ?

  • A 𝐢 𝐷
  • B 𝐴 𝐢
  • C 𝐴 𝐡
  • D 𝐴 𝐷
  • E 𝐡 𝐢

Q7:

Find the measure of ∠ 𝐡 , given 𝐴 𝐡 𝐢 𝐷 is an isosceles trapezium where 𝐴 𝐡 = 𝐴 𝐷 = 𝐷 𝐢 = 1 3 c m and 𝐡 𝐢 = 1 7 c m giving the answer to the nearest second.

  • A 8 1 9 β€² ∘
  • B 8 3 9 β€² ∘
  • C 8 0 9 β€² ∘
  • D 8 2 9 β€² ∘

Q8:

Find the measure of ∠ 𝐡 , given 𝐴 𝐡 𝐢 𝐷 is an isosceles trapezium where 𝐴 𝐡 = 𝐴 𝐷 = 𝐷 𝐢 = 7 c m and 𝐡 𝐢 = 9 c m giving the answer to the nearest second.

  • A 8 1 4 7 β€² 1 2 β€² β€² ∘
  • B 8 3 4 7 β€² 1 2 β€² β€² ∘
  • C 8 0 4 7 β€² 1 2 β€² β€² ∘
  • D 8 2 4 7 β€² 1 2 β€² β€² ∘

Q9:

In the given figure, 𝐴 𝐢 = 5 , 𝐡 𝐢 = 7 , and π‘š ∠ 𝐡 𝐢 𝐴 = 4 1 ∘ .

Calculate the height 𝐴 𝐷 to 2 decimal places.

Calculate the area of the triangle 𝐴 𝐡 𝐢 to 2 decimal places.

Q10:

Find s i n 𝐴 given 𝐴 𝐡 𝐢 is a right-angled triangle at 𝐡 where the point 𝐷 lies on 𝐡 𝐢 , 𝐷 𝐸 is perpendicular to 𝐴 𝐢 , 𝐷 𝐸 = 1 8 c m and 𝐢 𝐸 = 2 4 c m .

  • A 4 5
  • B 3 5
  • C 5 4
  • D 4 3

Q11:

A 33 ft ladder leans against a building such that the angle between the ground and the ladder is 8 0 ∘ . How high does the ladder reach up the side of the building?

Q12:

The distance between two villages 𝐴 and 𝐡 is 13 km where 𝐴 is west of 𝐡 . Village 𝐢 is located 3 7 ∘ east of north of 𝐴 and 4 8 ∘ north of west of 𝐡 . Find the distance between 𝐡 and 𝐢 giving the answer to the nearest kilometre.

Q13:

The base of a truck is 2 feet off the ground and a 15-foot ramp is used to load the truck. Find the angle the ramp makes with the horizontal ground.

Q14:

𝐴 , 𝐡 , and 𝐢 are three towns that lie in the same horizontal plane. 𝐡 lies 38 km southwest of 𝐴 . 𝐴 lies 2 3 ∘ east of north of 𝐢 and 𝐡 lies 7 ∘ east of north of 𝐢 . Find the length of 𝐴 𝐢 giving the answer to the nearest kilometre.

Q15:

In the given figure, π‘š ∠ 𝐡 𝐴 𝐢 = 9 0 ∘ and 𝐴 𝐷 βŠ₯ 𝐡 𝐢 . What is 𝐡 𝐢 πœƒ s i n ?

  • A 𝐴 𝐡
  • B 𝐢 𝐡
  • C 𝐴 𝐢
  • D 𝐢 𝐷
  • E 𝐴 𝐷

Q16:

𝐴 𝐡 𝐢 is a right-angled triangle at 𝐡 where π‘š ∠ 𝐢 = 6 5 4 8 β€² ∘ and 𝐴 𝐢 = 1 2 c m . Find the length of 𝐴 𝐡 giving the answer to two decimal places.

Q17:

Find the value of s i n s i n 𝑋 + π‘Œ given 𝑋 π‘Œ 𝑍 is a right-angled triangle at 𝑍 , 𝑋 π‘Œ = 5 8 c m , π‘Œ 𝑍 = 4 0 c m and 𝑋 𝑍 = 4 2 c m .

  • A 4 1 2 9
  • B 8 2 2 9
  • C 4 0 2 9
  • D 4 2 2 9

Q18:

In the given figure, 𝐴 𝐡 = 6 , 𝐡 𝐢 = 1 1 , and π‘š ∠ 𝐴 𝐡 𝐢 = 6 1 ∘ .

Calculate the height 𝐴 𝐷 to 2 decimal places.

Calculate the area of the triangle 𝐴 𝐡 𝐢 to 2 decimal places.

Q19:

In the given figure, 𝐴 𝐢 = 5 , 𝐡 𝐢 = 7 , and π‘š ∠ 𝐡 𝐢 𝐴 = 4 1 ∘ . Work out the height 𝐴 𝐷 of the triangle to 2 decimal places.

Q20:

Find s i n 𝐴 , given 𝐴 𝐡 𝐢 is a right-angled triangle at 𝐢 where 𝐴 𝐡 = 2 0 c m and 𝐡 𝐢 = 1 6 c m .

  • A 4 5
  • B 3 5
  • C 5 3
  • D 5 4

Q21:

A mountain has a uniform incline of 2 8 ∘ . If a person walks 127 metres to the peak of the mountain, how tall is the mountain? Give the answer to the nearest metre.

Q22:

What is the value of s i n πœƒ in the given triangle?

  • A 5 1 3
  • B 1 3 5
  • C 1 2 1 3
  • D 1 3 1 2
  • E 5 1 2

Q23:

Find the area of the triangle 𝐴 𝐡 𝐢 given 𝐴 𝐡 = 𝐴 𝐢 = 2 1 c m and 𝐡 𝐢 = 2 0 c m . Give the answer to two decimal places.

  • A 184.66 cm2
  • B 369.32 cm2
  • C 100 cm2
  • D 210 cm2

Q24:

Find π‘š ∠ 𝐡 𝐴 𝐢 giving the answer to the nearest second.

  • A 4 5 3 5 β€² 5 β€² β€² ∘
  • B 3 5 3 2 β€² 1 6 β€² β€² ∘
  • C 5 4 2 7 β€² 4 4 β€² β€² ∘
  • D 4 4 2 4 β€² 5 5 β€² β€² ∘

Q25:

Find π‘š ∠ 𝐡 𝐴 𝐢 giving the answer to the nearest second.

  • A 1 9 2 8 β€² 1 6 β€² β€² ∘
  • B 1 8 2 6 β€² 6 β€² β€² ∘
  • C 7 1 3 3 β€² 5 4 β€² β€² ∘
  • D 7 0 3 1 β€² 4 4 β€² β€² ∘
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