MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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6.2 Trigonometry of Right Triangles

Focus on right triangle sine and tangent ratio.

Before you solve

Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Trig ratios in a right triangleWorked steps · five questions02Special triangles: 30°, 45°, 60°Worked steps · five questions03Finding an unknown sideWorked steps · five questions04Solving a right triangleWorked steps · five questions05Applications: angles of elevation and depressionWorked steps · five questions
Lesson brief and rules

6.2 Trigonometry of Right Triangles

sin⁡θ=\sin \theta = opposite/hypotenuse; cos⁡θ=\cos \theta = adjacent/hypotenuse.

Worked example 11
01 / A right triangle has opposite side 1212 and hypotenuse 2020. Find sin⁡θ\sin \theta .
02 / sin⁡θ=\sin \theta = opposite/hypotenuse =1220=35=\dfrac{12}{20}=\dfrac{3}{5}.
03 / Answer: 35\dfrac{3}{5}
Worked example 2 · Tangent ratio

A right triangle has opposite side 1212 and adjacent side 1616. Find tan⁡θ\tan \theta .

Tangent is opposite over adjacent. Answer: 34\dfrac{3}{4}

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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