Enter the base and area, one side and an angle, or all three sides to calculate the height of a triangle.
If the base is \( b \) and the area is \( A \), the height \( h \) is: \( h = \frac{2A}{b} \)
If the known side is \( a \), and the angle \( C \) forms a perpendicular with the height, the height \( h \) is: \( h = a \times \sin(C) \)
If the sides of the triangle are \( a \), \( b \), and \( c \). Calculate the semi-perimeter \( s \): \( s = \frac{a + b + c}{2} \) Use Heron's formula to find the area \( A \): \( A = \sqrt{s \times (s - a) \times (s - b) \times (s - c)} \) Calculate the height \( h \) using the base \( b \): \( h = \frac{2A}{b} \)
Solution:
\( h = \frac{2 \times 25}{10} = 5 \)
Result: The height is 5.
Solution:
\( h = 8 \times \sin(30^\circ) = 8 \times 0.5 = 4 \)
Result: The height is 4.
Solution:
Calculate the semi-perimeter \(s\):
\( s = \frac{7 + 8 + 9}{2} = 12 \)
Calculate the area \(A\):
\( A = \sqrt{12 \times (12 - 7) \times (12 - 8) \times (12 - 9)} = \sqrt{720} \approx 26.83 \)
Calculate the height \(h\):
\( h = \frac{2 \times 26.83}{7} \approx 7.66 \)
Result: The height is approximately 7.66.