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

Start Practicing

Worksheet: Finding Values for Trigonometric Functions in Right Triangles

Q1:

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

Q2:

Find c o t 𝐡 given that 𝐴 𝐡 𝐢 is a right triangle at 𝐢 , where 𝐴 𝐢 = 1 2 c m and 𝐡 𝐢 = 9 c m .

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

Q3:

Find the main trigonometric ratios of given is a right triangle at where the ratio between and is .

  • A , ,
  • B , ,
  • C , ,
  • D , ,

Q4:

Find given that is a right triangle at where and .

  • A
  • B
  • C
  • D

Q5:

Find the values of π‘₯ and 𝑦 giving the answer to three decimal places.

  • A π‘₯ = 1 6 . 6 4 3 c m , 𝑦 = 8 . 9 9 9 c m
  • B π‘₯ = 8 . 9 9 9 c m , 𝑦 = 1 0 . 7 2 5 c m
  • C π‘₯ = 8 . 9 9 9 c m , 𝑦 = 1 6 . 6 4 3 c m
  • D π‘₯ = 1 0 . 7 2 5 c m , 𝑦 = 8 . 9 9 9 c m

Q6:

In the triangle shown, is the side labelled 𝑦 adjacent to angle πœƒ , opposite angle πœƒ , or the hypotenuse?

  • Ahypotenuse
  • Bopposite
  • Cadjacent

Q7:

Find the values of π‘₯ and 𝑦 giving the answer to three decimal places.

  • A π‘₯ = 4 7 . 4 3 2 c m , 𝑦 = 3 8 . 2 8 5 c m
  • B π‘₯ = 3 8 . 2 8 5 c m , 𝑦 = 2 6 . 1 1 0 c m
  • C π‘₯ = 3 8 . 2 8 5 c m , 𝑦 = 4 7 . 4 3 2 c m
  • D π‘₯ = 2 6 . 1 1 0 c m , 𝑦 = 3 8 . 2 8 5 c m

Q8:

𝑋 π‘Œ 𝑍 is a right-angled triangle at π‘Œ , where 𝑋 π‘Œ = 1 6 . 5 c m , π‘Œ 𝑍 = 2 8 c m , and 𝑋 𝑍 = 3 2 . 5 c m . Find the measure of ∠ 𝑍 giving the answer to the nearest second.

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

Q9:

Find the value of s i n c o s 𝐡 + 𝐢 , given that 𝐴 𝐡 𝐢 is a triangle, where 𝐴 𝐡 = 𝐴 𝐢 = 4 1 c m , 𝐡 𝐢 = 1 8 c m , and  𝐴 𝐷 is drawn perpendicular to 𝐡 𝐢 intersecting at 𝐷 .

  • A 4 1 4 9
  • B 1 1 8 0 3 6 9
  • C 3 6 9 9 8 2
  • D 4 9 4 1

Q10:

Find the value of given is a right triangle at where .

  • A600
  • B175
  • C625
  • D168

Q11:

𝐸 is a point inside a square 𝐴 𝐡 𝐢 𝐷 with a side length of 48 cm, where 𝐡 𝐸 = 𝐢 𝐸 and 𝑂 𝐸 = 3 0 c m . Find the value of 𝐾 , given that 𝐾 ( 𝑋 βˆ’ 𝑋 ) = 1 3 0 c o s s i n .

  • A 1 4 2
  • B6
  • C42
  • D 1 6

Q12:

The mayor of a city decided to build a new subway station at point 𝐷 between two existing stations at points 𝐡 and 𝐢 . The distance between 𝐷 and 𝐡 is 2.1 km, and the shortest distance between 𝐷 and the library at point 𝐴 is 3.1 km. Find the distance between points 𝐷 and 𝐢 , given that 𝐴 𝐢 and 𝐴 𝐡 are orthogonal. Give your answer to two decimal places.

  • A 5.54 km
  • B 2.09 km
  • C 2.57 km
  • D 4.58 km

Q13:

For the given figure, find the lengths of 𝐴 𝐡 and 𝐴 𝐢 . Give your solutions to two decimal places.

  • A 𝐴 𝐡 = 5 . 3 1 , 𝐴 𝐢 = 8 . 4 7
  • B 𝐴 𝐡 = 8 . 8 3 , 𝐴 𝐢 = 4 . 6 9
  • C 𝐴 𝐡 = 4 . 4 6 , 𝐴 𝐢 = 8 . 9 5
  • D 𝐴 𝐡 = 4 . 6 9 , 𝐴 𝐢 = 8 . 8 3
  • E 𝐴 𝐡 = 4 . 6 9 , 𝐴 𝐢 = 1 8 . 8 1

Q14:

Find , given is a right triangle at and .

  • A
  • B
  • C
  • D

Q15:

In the triangle shown, would we call the side labelled 𝑧 the hypotenuse, the adjacent side to angle πœƒ , or the side opposite angle πœƒ ?

  • Aadjacent side to angle πœƒ
  • Bopposite angle πœƒ
  • Chypotenuse

Q16:

In the figure, which of the following words describe the position of the side labelled π‘₯ with respect to the angle πœƒ ?

  • Ahypotenuse
  • Badjacent
  • Copposite

Q17:

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

  • A
  • B
  • C
  • D

Q18:

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

  • A
  • B
  • C
  • D

Q19:

𝐴 𝐡 𝐢 is an isosceles triangle where 𝐴 𝐡 = 𝐴 𝐢 = 1 7 c m and 𝐡 𝐢 = 3 0 c m . Find the value of t a n 𝐢 𝐴 𝐷 given 𝐷 lies on the midpoint of 𝐡 𝐢 where  𝐴 𝐷 βŠ₯ 𝐡 𝐢 .

  • A 1 5 1 7
  • B 8 1 5
  • C 1 7 1 5
  • D 1 5 8

Q20:

Find , given that is an isosceles trapezoid, where , , , and .

  • A18
  • B3
  • C9
  • D15
  • E25

Q21:

Find the value of given and .

  • A
  • B
  • C
  • D

Q22:

During a sandstorm, a tree which was growing perpendicular to the ground snapped at a point in its trunk. The top part of the tree fell and hit the ground so that it was 2 meters from the base of the tree. However, at the point of the break, the tree remained connected. The angle the fallen part of the tree made with the horizontal was . Find the original height of the tree giving the answer to the nearest meter.

  • A 3 m
  • B 4 m
  • C 5 m
  • D 7 m
  • E 1 m

Q23:

Rupert rests a 6 m ladder against a wall which is perpendicular to the ground. He measures that the base of the ladder is exactly 1.5 m from the base of the wall. Determine the height, β„Ž , where the top of the ladder touches the wall, the angle between the base of the ladder and the ground, πœƒ , and the angle between the top of the ladder and the wall, πœ™ . Give all of your answers accurate to two decimal places.

  • A β„Ž = 5 . 8 1 m , πœƒ = 1 4 . 4 8 ∘ , πœ™ = 7 5 . 5 2 ∘
  • B β„Ž = 1 . 4 5 m , πœƒ = 7 5 . 5 2 ∘ , πœ™ = 1 4 . 4 8 ∘
  • C β„Ž = 2 3 . 2 3 m , πœƒ = 7 5 . 5 2 ∘ , πœ™ = 1 4 . 4 8 ∘
  • D β„Ž = 5 . 8 1 m , πœƒ = 7 5 . 5 2 ∘ , πœ™ = 1 4 . 4 8 ∘
  • E β„Ž = 2 3 . 2 3 m , πœƒ = 1 4 . 4 8 ∘ , πœ™ = 7 5 . 5 2 ∘

Q24:

Find the value of s i n c o s 𝐡 + 𝐢 .

  • A 1 2 2 5
  • B 8 5
  • C 7 5
  • D 6 5