Lesson 10

Solving Problems with Trigonometry

  • Let’s solve problems about right triangles.

Problem 1

Technology required. Find the area of the isosceles trapezoid. 

Isosceles trapezoid. Bases 1 and 2 = 10 and 15 units. Base angles = 40 degrees 

Problem 2

Technology required. The sun is 62 degrees above the horizon. A tree casts a shadow that is 12 feet long. How tall is the tree? 

Right triangle. Height = tree height. Bottom side = shadow formed from tree = 12 units. Hypotenuse from top of tree to end of shadow.

Problem 3

Technology required. A plane leaves the ground with an elevation angle of 6 degrees. The plane travels 10 miles horizontally.

  1. How high is the plane at the time? 
  2. What is the distance of the plane’s path? 

Problem 4

Technology required. Find the missing measurements.

Right triangle A B D. A B is 10 units and B D is 3 units. Angle B A D is labeled theta and angle A D B is labeled alpha.
(From Unit 4, Lesson 9.)

Problem 5

Technology required. Ramps in a parking garage need to be both steep and safe. The maximum safe incline for a ramp is 8.5 degrees. 

Is this a safe ramp? Explain or show your reasoning.

Right triangle. Base 100 units, height 20 units. A car is drawn above the hypotenuse.
(From Unit 4, Lesson 9.)

Problem 6

Select all true equations. 











(From Unit 4, Lesson 8.)

Problem 7

Technology required. Clare is flying a kite. She gets tired, so she stakes the kite into the ground. The kite is on a string that is 30 ft long and makes a 27 degree angle with the ground. How high is the kite?


30 ft


13.6 ft


26.7 ft


15.3 ft

(From Unit 4, Lesson 7.)

Problem 8

What is the length of the diagonal?

Square. Side length labeled 4.
(From Unit 4, Lesson 2.)