Lesson 5

Working with Ratios in Right Triangles

  • Let’s solve problems about right triangles.

Problem 1

A triangle has sides with lengths 8, 15, and 17.

  1. Verify this is a Pythagorean triple.
  2. Approximate the acute angles in this triangle.

Problem 2

Kiran is flying a kite. He gets tired, so he stakes the kite into the ground. The kite is on a string that is 18 feet long and makes a 30 degree angle with the ground. How high is the kite?

String = hypotenuse = 18 feet. angle with the ground = 30 degrees. Perpendicular height unknown.

Problem 3

Triangle \(ABC\) has a right angle at \(C\). Select all measurements which would mean it has a hypotenuse with a length of 10 units. 

Triangle A B C with angle C marked as a right angle.

Angle \(A\) is 20 degrees, \(BC\) is 2 units


\(AC\) is 7 units, \(BC\) is 3 units


Angle \(B\) is 50 degrees, \(BC\) is 4 units


Angle \(A\) is 30 degrees, \(BC\) is 5 units


\(AC\) is 8 units, \(BC\) is 6 units

Problem 4

What is a reasonable approximation for angle \(B\) if the ratio of the adjacent leg divided by the hypotenuse is 0.45?


27 degrees


30 degrees


60 degrees


63 degrees

(From Unit 4, Lesson 4.)

Problem 5

Estimate the values to complete the table.

Right triangle ABC. Right angle at B.
angle adjacent leg \(\div\) hypotenuse opposite leg \(\div\) hypotenuse opposite leg \(\div\) adjacent leg
\(A\) 0.31 0.95 3.1
(From Unit 4, Lesson 4.)

Problem 6

What is the length of side \(AB\)?

Right triangle A B C. A C is 6 units, angle B A C is 90 degrees, and angle A C B is 30 degrees.
(From Unit 4, Lesson 3.)

Problem 7

What is the length of the square’s side? 

Square with diagonal = 6 units 

3 units


\(\frac{6}{\sqrt2}\) units


\(6 \sqrt2\) units


12 units

Problem 8

Find the lengths of segments \(AD\) and \(BD\). Then check your answers using a different method. 

Right triangle A B C. Altitude B D drawn, creating right triangle B D C. Segment D C labeled 12. Segment B C labeled 13.
(From Unit 3, Lesson 13.)