TAN function: calculate mast or roof height from horizontal run and angle

Turn horizontal run and sight angle into vertical height

In right-triangle surveying and roof framing, TAN(angle) = Opposite (Rise) / Adjacent (Run). Standing 40 m from a tower with a 45° sight angle and 1.6 m instrument height gives 40 * TAN(RADIANS(45)) + 1.6 = 41.6 m.

The example assumes level ground and a horizontal distance to the tower base. Measurements close to 90 degrees are extremely sensitive to angle error, even when they do not equal 90 exactly.

Calculate total structure height

Because TAN(RADIANS(45)) = 1, rise equals run (40 m), plus 1.6 m eye level = 41.6 m.

=ROUND(A2 * TAN(RADIANS(B2)) + C2, 2)

Guard 90° vertical angles where tangent is undefined

At ±90°, cosine is zero in exact math (and ~6.12E-17 in floating-point radians, producing ~1.63E+16). Guarding MOD(ABS(B2), 180)=90 flags vertical sightlines cleanly.

=IF(MOD(ABS(B2), 180)=90, "Vertical undefined", ROUND(A2 * TAN(RADIANS(B2)) + C2, 2))

Further reading

• Microsoft Support — TAN function