Trigonometry Applications
Trigonometry uses the ratios of sides in right-angled triangles — sine, cosine, and tangent — to find unknown sides and angles. It has applications in navigation, architecture, and engineering.
What You Need to Know
Key Concept Diagram
SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent
To find an unknown side, choose the trig ratio that links the known and unknown sides
To find an unknown angle, use the inverse trig function (sin^-1, cos^-1, tan^-1)
The hypotenuse is always opposite the right angle and is the longest side
Key Vocabulary
Hypotenuse
The longest side of a right-angled triangle, opposite the right angle
Opposite
The side directly across from the reference angle in a right triangle
Adjacent
The side next to the reference angle that is not the hypotenuse
SOH-CAH-TOA
A mnemonic for the three trigonometric ratios: sin, cos, tan
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
In a right triangle, the angle is 35 degrees and the hypotenuse is 12 cm. Find the opposite side. (sin 35 = 0.574)
Question 2
A ladder 5 m long leans against a wall, making an angle of 60 degrees with the ground. How high up the wall does it reach? (sin 60 = 0.866)
Question 3
tan(angle) = 0.75 in a right triangle. What is the angle? (tan^-1(0.75) = 36.9 degrees)
Key Concepts Summary
- ●SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent
- ●To find an unknown side, choose the trig ratio that links the known and unknown sides
- ●To find an unknown angle, use the inverse trig function (sin^-1, cos^-1, tan^-1)
- ●The hypotenuse is always opposite the right angle and is the longest side