Topic Content:
- Using Tangent Ratio to find an Angle
If the opposite and the adjacent sides of an unknown angle of a right-angled triangle are given, we can use the tan ratio to calculate the angle.
Using: SOH CAH TOA
where:
S = Sine, C = Cosine, T = Tan
O = Opposite, A = Adjacent, H = Hypotenuse
tan θ = \( \frac {Opposite \: side}{Adjacent \: side} \)
The inverse tan formula is used to find the angle in a right-angled triangle when the opposite and adjacent sides are given.
θ = \( \scriptsize tan^{-1} \normalsize \left (\frac {opposite \: side}{adjacent \: side} \right) \)
For example:
| angle | ratio |
| tan 35° | 0.7002 |
| ratio | angle |
| tan-1 (0.7002) | 35° |
On a calculator, you can find the inverse of tangent by using ” tan⁻¹ ” button.
On some calculators, the function is on the same key on the calculator as the tan function (shift tan).
Example 2.2.1:
Use the tangent ratio to calculate the marked angle in the following triangles correct to 1 d.p.
All measurements are in cm.
1.
tan θ = \( \frac {Opposite}{Adjacent} \)
tan θ = \( \frac {4}{9} \)
tan θ = 0.4444
θ = tan-1 (0.4444)
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