Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ ) - Right Triangle Trigonometry

Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )

Tangent ratio is yet another trigonometric ratio for right-angled triangles. Tangent ratio is the ratio of opposite side to adjacent side of a right triangle. Same as the sine and cosine ratios, tangent ratios can be used to calculate the angles and sides of right angle triangles.

Basic Concepts
Pythagorean theorem
ASTC rule in trigonometry (All Students Take Calculus)

Related Concepts
Law of sines
Law of cosines
Find the exact value of trigonometric ratios
Unit circle

Lessons

3.
Determine the angles and sides using Tangent

Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )

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Intro Lesson

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Lesson: 3a

Lesson: 3b

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Lessons

Intro Lesson

What are sine, cosine and tangent?

1.

Determine each tangent ratio using a calculator i) tan⁡70∘\tan 70^\circ tan70∘ ii) tan⁡−134∘\tan-134^\circtan−134∘

2.

Determine the angle to the nearest degree using a a calculator i) tan⁡θ=0.64\tan \theta = 0.64tanθ=0.64 ii) tan⁡θ=−1.45\tan \theta = -1.45tanθ=−1.45

3.

Determine the angles and sides using Tangent

a)

Find angle A and B:

b)

Find the value of "x" using tangent

c)

Find the value of "x" using tangent

4.

Draw and label a right triangle to illustrate tangent ratio, then calculate the angle.

a)

tan⁡θ=59\tan \theta = {5 \over 9}tanθ=95​

Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a}ao​ )

Don't just watch, practice makes perfect.

We have over 250 practice questions in Trigonometry for you to master.

Geometry
Pythagorean theorem

Trigonometry
ASTC rule in trigonometry (All Students Take Calculus)

or

Determine each tangent ratio using a calculator
i) $\tan 70^\circ$
ii) $\tan-134^\circ$

Determine the angle to the nearest degree using a a calculator
i) $\tan \theta = 0.64$
ii) $\tan \theta = -1.45$

$\tan \theta = {5 \over 9}$

Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )