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Worksheet: Finding a Missing Side Length in a Right Triangle Using Trigonometric Ratios

Q1:

Find the length of 𝐡 𝐢 giving the answer to two decimal places.

Q2:

Find the length of 𝐡 𝐢 giving the answer to two decimal places.

Q3:

Find the length of 𝐡 𝐢 giving the answer to two decimal places.

Q4:

Find π‘₯ to two decimal places.

Q5:

Find π‘₯ to two decimal places.

Q6:

A 23 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?

Q7:

Given the following figure, find the lengths of 𝐴 𝐢 and 𝐡 𝐢 and the measure of ∠ 𝐴 𝐡 𝐢 in degrees. Give your answers to two decimal places.

  • A 𝐴 𝐢 = 7 . 6 2 , 𝐡 𝐢 = 8 . 1 9 , π‘š ∠ 𝐴 𝐡 𝐢 = 7 0 . 0 0 ∘
  • B 𝐴 𝐢 = 7 . 3 2 , 𝐡 𝐢 = 7 . 9 1 , π‘š ∠ 𝐴 𝐡 𝐢 = 7 2 . 0 0 ∘
  • C 𝐴 𝐢 = 7 . 9 5 , 𝐡 𝐢 = 8 . 1 9 , π‘š ∠ 𝐴 𝐡 𝐢 = 6 0 . 0 0 ∘
  • D 𝐴 𝐢 = 7 . 8 2 , 𝐡 𝐢 = 8 . 3 7 , π‘š ∠ 𝐴 𝐡 𝐢 = 6 9 . 0 0 ∘
  • E 𝐴 𝐢 = 7 . 2 2 , 𝐡 𝐢 = 7 . 8 2 , π‘š ∠ 𝐴 𝐡 𝐢 = 6 9 . 0 0 ∘

Q8:

Find the length of given is a right triangle at where and .

  • A 26 cm
  • B 10 cm
  • C 162 cm
  • D 32 cm
  • E 31 cm

Q9:

A kite, which is at a perpendicular height of 44 m, is attached to a string inclined at 6 0 ∘ to the horizontal. Find the length of the string accurate to one decimal place.

Q10:

A kite, which is at a perpendicular height of 51 m, is attached to a string inclined at 5 5 ∘ to the horizontal. Find the length of the string accurate to one decimal place.

Q11:

A kite, which is at a perpendicular height of 48 m, is attached to a string inclined at 2 9 ∘ to the horizontal. Find the length of the string accurate to one decimal place.

Q12:

A builder leans a 6-foot plank of wood against a vertical wall. If one end of the plank is 1.5 feet from the bottom of the wall, what is the angle between the plank and the wall?

Q13:

The angle of elevation between an aeroplane 10 000 m high and a person on a point on the ground is . Find the distance between the point and the aeroplane giving the answer to the nearest metre.

Q14:

A kite has a string of length 75 meters. The angle the string makes with the horizontal ground is 5 3 ∘ . Find the height of the kite from the ground giving the answer to two decimal places.

Q15:

In the given figure, find π‘₯ . Give your answer to two decimal places.

Q16:

Find the length of 𝐴 𝐢 , given that 𝐴 𝐡 = 1 9 c m , 𝐷 𝐸 = 1 1 c m , and 𝐢 𝐸 = 2 1 c m .

  • A 2 3 1 2 9 cm
  • B 3 1 9 2 1 cm
  • C 6 0 9 8 cm
  • D 3 9 9 1 1 cm
  • E 1 1 3 9 9 cm

Q17:

A person observes a point on the ground from the top of a hill that is 1.56 km high. The angle of depression is 2 9 ∘ . Find the distance between the point and the observer giving the answer to the nearest metre.