SME
Grade 10 Math · Problem type
Find an angle from two sides
Use this for “A ramp rises 1.5 m over a run of 6 m. What angle does it make with the ground?”
Diagram
sin A = o/c = 1.5/6.18 ≈ 0.2425
cos A = r/c = 6/6.18 ≈ 0.9701
tan A = o/r = 1.5/6 ≈ 0.25
This is an example. Type your own values to start a new problem.
tan(
A
°)
=
o
r
Formulas
tan(
A
°)
=
o
r
tan(14.0362°)
=
1.5
6
Assumptions
•
The rise is opposite the angle A and the run is adjacent to it, so tan A = rise ÷ run.
•
The inverse tangent, tan⁻¹, turns the ratio back into the angle.
•
Set the calculator to degrees.
Step-by-step
WE KNOW
o = 1.5 m, r = 6 m
FIND
ramp angle (A)
Step 1 · Find ramp angle (A)
Use tan(A°) = o ÷ r
The inverse tangent turns the ratio back into the angle.
A
=
tan⁻¹(
o
r
)
A
=
tan⁻¹(
1.5
6
)
A
=
14.0362°
Check
Put the numbers back in. Both sides should match.
tan(14.0362°)
=
1.5
6
✓
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Right-triangle trigonometry: sine, cosine and tangent
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