Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Finding Angles Using the Sine and Cosine Ratios

Q1:

Find the value of 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 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 𝐡 𝐢
  • B 𝐴 𝐡
  • C 𝐴 𝐷
  • D 𝐢 𝐷
  • E 𝐴 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 2 9 β€² ∘
  • B 8 3 9 β€² ∘
  • C 8 0 9 β€² ∘
  • D 8 1 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 2 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 1 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 given is a right triangle at where point lies on , is perpendicular to , cm, and cm.

  • A
  • B
  • C
  • D

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 kilometer.

  • A 41 km
  • B 8 km
  • C 16 km
  • D 11 km

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

Q16:

is a right triangle at where and . Find the length of giving the answer to two decimal places.

  • A 26.70 cm
  • B 4.92 cm
  • C 13.16 cm
  • D 10.95 cm

Q17:

Find the value of given is a right triangle at , , and .

  • A
  • B
  • C
  • D

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 , given is a right triangle at where and .

  • A
  • B
  • C
  • D

Q21:

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

  • A 112 m
  • B 68 m
  • C 239 m
  • D 60 m
  • E 271 m

Q22:

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

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

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

Q24:

Find giving the answer to the nearest second.

  • A
  • B
  • C
  • D

Q25:

Find giving the answer to the nearest second.

  • A
  • B
  • C
  • D