Worksheet: The Sine Ratio

In this worksheet, we will practice finding angles and sides in a right triangle using the sine ratio.

Q1:

Find π‘šβˆ π΅π΄πΆ giving the answer to the nearest second.

  • A4535β€²5β€²β€²βˆ˜
  • B5427β€²44β€²β€²βˆ˜
  • C4424β€²55β€²β€²βˆ˜
  • D3532β€²16β€²β€²βˆ˜

Q2:

Find sin𝐴, given 𝐴𝐡𝐢 is a right triangle at 𝐢 where 𝐴𝐡=20cm and 𝐡𝐢=16cm.

  • A35
  • B53
  • C54
  • D45

Q3:

Find the measure of ∠𝐡, given 𝐴𝐡𝐢𝐷 is an isosceles trapezoid where 𝐴𝐡=𝐴𝐷=𝐷𝐢=13cm and 𝐡𝐢=17cm giving the answer to the nearest second.

  • A819β€²βˆ˜
  • B839β€²βˆ˜
  • C829β€²βˆ˜
  • D809β€²βˆ˜

Q4:

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

Q5:

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?

Q6:

In the given figure, π‘šβˆ π΅π΄πΆ=90∘ and 𝐴𝐷βŠ₯𝐡𝐢. What isπ΄πΆπœƒsin?

  • A𝐢𝐷
  • B𝐴𝐡
  • C𝐴𝐷
  • D𝐴𝐢
  • E𝐡𝐢

Q7:

Find sin𝐴 given 𝐴𝐡𝐢 is a right-angled triangle at 𝐡 where the point 𝐷 lies on 𝐡𝐢, 𝐷𝐸 is perpendicular to 𝐴𝐢, 𝐷𝐸=18cm and 𝐢𝐸=24cm.

  • A35
  • B54
  • C45
  • D43

Q8:

A 33 ft ladder leans against a building such that the angle between the ground and the ladder is 80∘. How high does the ladder reach up the side of the building?

Q9:

The distance between two villages 𝐴 and 𝐡 is 13 km where 𝐴 is west of 𝐡. Village 𝐢 is located 37∘ east of north of 𝐴 and 48∘ north of west of 𝐡. Find the distance between 𝐡 and 𝐢 giving the answer to the nearest kilometer.

Q10:

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.

Q11:

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.

Q12:

𝐴, 𝐡, and 𝐢 are three towns that lie in the same horizontal plane. 𝐡 lies 38 km southwest of 𝐴. 𝐴 lies 23∘ east of north of 𝐢 and 𝐡 lies 7∘ east of north of 𝐢. Find the length of 𝐴𝐢 giving the answer to the nearest kilometer.

Q13:

In the given figure, π‘šβˆ π΅π΄πΆ=90∘ and 𝐴𝐷βŠ₯𝐡𝐢. What is π΅πΆπœƒsin?

  • A𝐢𝐡
  • B𝐴𝐷
  • C𝐢𝐷
  • D𝐴𝐡
  • E𝐴𝐢

Q14:

𝐴𝐡𝐢 is a right-angled triangle at 𝐡 where π‘šβˆ πΆ=6548β€²βˆ˜ and 𝐴𝐢=12cm. Find the length of 𝐴𝐡 giving the answer to two decimal places.

Q15:

Find the value of sinsin𝑋+π‘Œ given π‘‹π‘Œπ‘ is a right-angled triangle at 𝑍, π‘‹π‘Œ=58cm, π‘Œπ‘=40cm and 𝑋𝑍=42cm.

  • A8229
  • B4029
  • C4129
  • D4229

Q16:

In the given figure, 𝐴𝐢=5, 𝐡𝐢=7, and π‘šβˆ π΅πΆπ΄=41∘. Work out the height 𝐴𝐷 of the triangle to 2 decimal places.

Q17:

In the given figure, 𝐴𝐡=6, 𝐡𝐢=11, and π‘šβˆ π΄π΅πΆ=61∘. Work out the height 𝐴𝐷 of the triangle to 2 decimal places.

Q18:

A mountain has a uniform incline of 28∘. If a person walks 127 meters to the peak of the mountain, how tall is the mountain? Give the answer to the nearest meter.

Q19:

What is the value of sinπœƒ in the given triangle?

  • A513
  • B512
  • C1312
  • D1213
  • E135

Q20:

A circle has a radius of 16 cm. A chord is drawn where the central angle is 80∘. Find the length of the chord giving the answer to three decimal places.

Q21:

Consider the following right triangle 𝐴𝐡𝐢.

Which of the following statements is true?

  • Asincos𝛼=𝑏𝑐,𝛼=π‘Žπ‘
  • Bsincos𝛼=π‘Žπ‘,𝛼=𝑏𝑐
  • Csincos𝛼=π‘π‘Ž,𝛼=π‘π‘Ž
  • Dsincos𝛼=π‘Žπ‘,𝛼=π‘Žπ‘
  • Esincos𝛼=π‘π‘Ž,𝛼=𝑐𝑏

Find the value of (𝛼)+(𝛼)sincos (usually written as: sinοŠ¨οŠ¨π›Ό+π‘π‘œπ‘ π›Ό).

  • Aο€»π‘π‘Žο‡+𝑐𝑏=𝑏𝑐+π‘Žπ‘π‘Žπ‘οŠ¨οŠ¨οŠ¨οŠ¨οŠ¨οŠ¨οŠ¨οŠ¨
  • Bο€»π‘Žπ‘ο‡+𝑏𝑐=π‘Ž+𝑏𝑐=𝑐𝑐=1
  • Cο€»π‘Žπ‘ο‡+𝑐𝑏=π‘Ž+π‘π‘οŠ¨οŠ¨οŠ¨οŠ¨οŠ¨
  • Dο€»π‘Žπ‘ο‡+ο€»π‘Žπ‘ο‡=π‘Žο€Ήπ‘+π‘ο…π‘π‘οŠ¨οŠ¨οŠ¨οŠ¨οŠ¨οŠ¨οŠ¨
  • Eο€½π‘π‘Žο‰+ο€»π‘π‘Žο‡=𝑏+π‘π‘Ž=2π‘βˆ’π‘Žπ‘ŽοŠ¨οŠ¨οŠ¨οŠ¨οŠ¨οŠ¨οŠ¨οŠ¨

Q22:

In the given figure, 𝐡𝐴 has been extended to the point 𝐷 such that 𝐡𝐷 and 𝐷𝐢 are perpendicular. Work out the length of 𝐷𝐢 to two decimal places.

Q23:

What is the value of sinπœƒ in the given triangle?

  • A34
  • B35
  • C53
  • D43
  • E45

Q24:

An airplane is flying to a city 200 miles away. Given that the destination city is 25 miles north of the departure city, how many degrees north of east should the airplane fly? Round your answer to two decimal places.

Q25:

Find π‘šβˆ π΄ given 𝐴𝐡𝐢𝐷 is an isosceles trapezoid where 𝐴𝐡=𝐴𝐷=𝐷𝐢=15cm and 𝐡𝐢=33cm. Give the answer to the nearest second.

  • A12752β€²12β€²β€²βˆ˜
  • B12652β€²12β€²β€²βˆ˜
  • C12852β€²12β€²β€²βˆ˜
  • D12552β€²12β€²β€²βˆ˜

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