Trigonometry Applications
Trigonometry is applied to real-world problems involving angles of elevation and depression, bearings, and distances that cannot be measured directly.
What You Need to Know
Key Concept Diagram
Angle of elevation is measured upward from the horizontal to an object above
Angle of depression is measured downward from the horizontal to an object below
SOHCAHTOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj
Draw a clear diagram labelling the right angle, known angle, and sides before calculating
Key Vocabulary
Angle of elevation
The angle measured upward from the horizontal line of sight to an object
Angle of depression
The angle measured downward from the horizontal line of sight to an object
Bearing
A direction measured clockwise from north, given as a three-digit number
Hypotenuse
The longest side of a right triangle, opposite the right angle
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A person stands 40 m from the base of a tree. The angle of elevation to the top is 30°. What is the height of the tree?
Question 2
Which trigonometric ratio connects the opposite side and the hypotenuse?
Question 3
A ship is on a bearing of 090°. What direction is it travelling?
Key Concepts Summary
- ●Angle of elevation is measured upward from the horizontal to an object above
- ●Angle of depression is measured downward from the horizontal to an object below
- ●SOHCAHTOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj
- ●Draw a clear diagram labelling the right angle, known angle, and sides before calculating