Right Triangle Base and Hypotenuse from Angle and Height

Enter an acute angle and the height (opposite side) to find a right triangle base, hypotenuse, area, and trig ratios.

Input

Enter the acute angle and the height (its opposite side) to compute the base, hypotenuse, area, and trig ratios.

Angle unit

Angle θ

deg

Height (opposite θ)

length

Base

8.66025404

Hypotenuse

Area

21.65063509

Perimeter

23.66025404

Height

Angle θ

30 deg

Other acute angle

60 deg

Trig ratios of θ

sin

0.5

cos

0.8660254

tan

0.57735027

csc

sec

1.15470054

cot

1.73205081

Base equals height divided by tan θ, and hypotenuse equals height divided by sin θ. Area equals base times height divided by 2.

The right angle sits at the lower left. The height h is the vertical side (opposite the acute angle), the base is the horizontal side, and the hypotenuse is the remaining side.
The base equals height divided by tan of the angle, and the hypotenuse equals height divided by sin of the angle, based on tan equals height over base and sin equals height over hypotenuse.
Area equals base times height divided by 2, and perimeter equals base plus height plus hypotenuse. The other acute angle equals 90 degrees minus the entered angle.
Enter an acute angle greater than 0 and less than 90 degrees. The height must be a positive value.
The angle unit can be degrees or radians. Radian input is converted to degrees internally to validate the allowed range.

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