测量计算器
Right Triangle Area from Leg and Angle
Enter leg b, hypotenuse c, and angle A to find the exact area of your right triangle.
面积变体 (角 A) 计算器
该计算器遵循 并得出 Area。
输入数值以计算 Area。
Area
结果-
计算步骤
公式:
What This Tool Solves
Enter one leg, the hypotenuse, and the included angle to calculate area using trigonometric formulas.
Use this calculator when you only know two sides and the included angle. This method uses trigonometry to find the exact area without needing the third side.
Known values
Leg b, hypotenuse c, and Angle A
Finds
Area (A)
Main formula
A = (b × c × sin(A)) / 2
Best for
Trigonometry problems, surveying, and cases missing the third side
Area Formula Using Sine
When you know two sides of any triangle and the angle between them, you can find the area using the sine rule for area: A = (1/2) * side1 * side2 * sin(angle).
In a right triangle where you know a leg, the hypotenuse, and the angle between them, this becomes A = (1/2) * b * c * sin(A).
Right Triangle Diagram: Area from Sine
The diagram shows the triangle with sides b and c forming the included angle A.
Diagram Key
a = opposite leg
Not required for this calculation.
b = adjacent leg
One of the known sides forming the angle.
c = hypotenuse
The other known side forming the angle.
A = Area
The area computed using trigonometric sine.
- Ensure the angle is entered in degrees.
- The formula A = 1/2 * ab * sin(C) applies to all triangles.
How to Calculate Area Using Sine
- Identify the leg, hypotenuse, and included angle.
- Enter leg b into the first input.
- Enter hypotenuse c into the second input.
- Enter angle A in degrees into the third input.
- Click Calculate to see the area.
Worked Example: Area Using Angle
If leg b is 4, hypotenuse c is 5, and angle A is 36.87°:
The area is 6 square units.
Why Use Trigonometry for Area?
Sometimes you cannot easily measure all three sides of a triangle, but measuring two sides and their included angle is possible (such as in land surveying).
This trigonometric approach gives the precise area without first having to solve the missing side using the Pythagorean theorem.
常见问题
关于直角三角形测量和面积的常见问题解答。
01 What if I know the other angle? expand_more
You can use A = (1/2) * a * c * sin(B) if you know leg a and angle B instead.