Lesson Worksheet: Right Triangle Trigonometry: Solving for an Angle Mathematics • 11th Grade

In this worksheet, we will practice finding a missing angle in a right triangle using the appropriate inverse trigonometric function given two side lengths.

Q1:

The height of a ski slope is 16 metres and the length is 20 metres. Find the measure of βˆ πœƒ giving the answer to two decimal places.

Q2:

For the given figure, find the measure of ∠𝐡𝐴𝐢, in degrees, to two decimal places.

Q3:

In the given figure, find the measure of angle πœƒ, in degrees, to two decimal places.

Q4:

For the given figure, find the measures of ∠𝐴𝐡𝐢 and ∠𝐴𝐢𝐡, in degrees, to two decimal places.

  • Aπ‘šβˆ π΄π΅πΆ=66.03∘, π‘šβˆ π΄πΆπ΅=23.96∘
  • Bπ‘šβˆ π΄π΅πΆ=63.61∘, π‘šβˆ π΄πΆπ΅=26.39∘
  • Cπ‘šβˆ π΄π΅πΆ=26.39∘, π‘šβˆ π΄πΆπ΅=63.61∘
  • Dπ‘šβˆ π΄π΅πΆ=26.57∘, π‘šβˆ π΄πΆπ΅=63.43∘
  • Eπ‘šβˆ π΄π΅πΆ=63.43∘, π‘šβˆ π΄πΆπ΅=26.57∘

Q5:

Find the values of 𝛼 and 𝛽 giving the answer to the nearest second.

  • A𝛼=4614β€²18β€²β€²βˆ˜, 𝛽=3550β€²16β€²β€²βˆ˜
  • B𝛼=3550β€²16β€²β€²βˆ˜, 𝛽=4614β€²18β€²β€²βˆ˜
  • C𝛼=4345β€²42β€²β€²βˆ˜, 𝛽=4614β€²18β€²β€²βˆ˜
  • D𝛼=4614β€²18β€²β€²βˆ˜, 𝛽=4345β€²42β€²β€²βˆ˜

Q6:

Given the following figure, find the measures of angles ∠𝐴𝐢𝐡 and ∠𝐡𝐴𝐢 and the length of 𝐴𝐢. Give your answers to two decimal places.

  • Aπ‘šβˆ π΄πΆπ΅=41.63∘, π‘šβˆ π΅π΄πΆ=48.37∘, 𝐴𝐢=9.43
  • Bπ‘šβˆ π΄πΆπ΅=41.63∘, π‘šβˆ π΅π΄πΆ=48.37∘, 𝐴𝐢=12.04
  • Cπ‘šβˆ π΄πΆπ΅=48.37∘, π‘šβˆ π΅π΄πΆ=41.63∘, 𝐴𝐢=9.43
  • Dπ‘šβˆ π΄πΆπ΅=48.37∘, π‘šβˆ π΅π΄πΆ=41.63∘, 𝐴𝐢=11.22
  • Eπ‘šβˆ π΄πΆπ΅=62.73∘, π‘šβˆ π΅π΄πΆ=27.27∘, 𝐴𝐢=10.63

Q7:

π‘‹π‘Œπ‘ is a right-angled triangle at π‘Œ, where π‘‹π‘Œ=16.5cm, π‘Œπ‘=28cm, and 𝑋𝑍=32.5cm. Find the measure of βˆ π‘ giving the answer to the nearest second.

  • A5929β€²23β€²β€²βˆ˜
  • B2655β€²0β€²β€²βˆ˜
  • C4044β€²46β€²β€²βˆ˜
  • D3030β€²37β€²β€²βˆ˜

Q8:

𝐴𝐡𝐢 is a right triangle at 𝐡, where 𝐡𝐢=10cm and 𝐴𝐢=18cm. Find the length 𝐴𝐡, giving the answer to the nearest centimeter, and the measure of angles 𝐴 and 𝐢, giving the answer to the nearest degree.

  • A𝐴𝐡=15cm, π‘šβˆ π΄=43∘, π‘šβˆ πΆ=47∘
  • B𝐴𝐡=15cm, π‘šβˆ π΄=34∘, π‘šβˆ πΆ=56∘
  • C𝐴𝐡=15cm, π‘šβˆ π΄=35∘, π‘šβˆ πΆ=55∘
  • D𝐴𝐡=15cm, π‘šβˆ π΄=42∘, π‘šβˆ πΆ=48∘

Q9:

A 5 m ladder is leaning against a vertical wall such that its base is 2 m from the wall. Work out the angle between the ladder and the floor, giving your answer to two decimal places.

  • A68.19∘
  • B23.57∘
  • C66.42∘
  • D21.80∘

Q10:

A car is going down a ramp that is 10 meters high and 71 meters long. Find the angle between the ramp and the horizontal, giving the answer to the nearest second.

  • A8154β€²12β€²β€²βˆ˜
  • B81β€²2β€²β€²βˆ˜
  • C85β€²48β€²β€²βˆ˜
  • D815β€²48β€²β€²βˆ˜
  • E6231β€²42β€²β€²βˆ˜

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