Lesson Worksheet: Right Triangle Trigonometry: Solving for a Side Mathematics • 11th Grade

In this worksheet, we will practice finding the value of a missing side length in a right triangle by choosing the appropriate trigonometric ratio for a given angle.

Q1:

Find π‘₯ to two decimal places.

Q2:

Find π‘₯ to two decimal places.

Q3:

Find the length of 𝐡𝐢 giving the answer to two decimal places.

Q4:

Given the following figure, find the lengths of 𝐴𝐢 and 𝐡𝐢 and the measure of ∠𝐡𝐴𝐢 in degrees. Give your answers to two decimal places.

  • A𝐴𝐢=10.23, 𝐡𝐢=9.42, π‘šβˆ π΅π΄πΆ=68.00∘
  • B𝐴𝐢=10.68, 𝐡𝐢=9.90, π‘šβˆ π΅π΄πΆ=69.00∘
  • C𝐴𝐢=10.34, 𝐡𝐢=9.53, π‘šβˆ π΅π΄πΆ=70.00∘
  • D𝐴𝐢=10.68, 𝐡𝐢=9.90, π‘šβˆ π΅π΄πΆ=68.00∘
  • E𝐴𝐢=10.57, 𝐡𝐢=9.78, π‘šβˆ π΅π΄πΆ=68.00∘

Q5:

Find the length of 𝐴𝐢, given that 𝐴𝐡𝐢 is a right triangle at 𝐡, where sin𝐢=916 and 𝐴𝐡=18cm.

Q6:

𝐴𝐡𝐢 is an isosceles triangle where 𝐴𝐡=𝐴𝐢=9cm, π΄π·βŸ‚π΅πΆ and π‘šβˆ πΆ=34∘. Find the length of 𝐡𝐢 giving the answer to one decimal place.

Q7:

A 23 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? Give your answer to two decimal places.

Q8:

A kite, which is at a perpendicular height of 44 m, is attached to a string inclined at 60∘ to the horizontal. Find the length of the string accurate to one decimal place.

Q9:

𝐴𝐡𝐢𝐷 is a rectangle where 𝐴𝐢=49.6cm and π‘šβˆ π΄πΆπ΅=2654β€²βˆ˜. Find the lengths of 𝐴𝐡 and 𝐡𝐢 giving the answer to three decimal places.

  • A𝐴𝐡=22.441cm, 𝐡𝐢=44.233cm
  • B𝐴𝐡=44.233cm, 𝐡𝐢=22.441cm
  • C𝐴𝐡=44.233cm, 𝐡𝐢=25.164cm
  • D𝐴𝐡=25.164cm, 𝐡𝐢=44.233cm

Q10:

A swimming pool is in the shape of a trapezoid. Find the area of the trapezoid giving the answer to the nearest square meter.

This lesson includes 31 additional questions and 189 additional question variations for subscribers.

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