Length C and B in the right angled triangle is 24 cm
And the length of A and B is 20cm while line d to a is 15cm. What is the are of the triangle bcd
To find the area of triangle BCD, we can use the formula for the area of a triangle given the lengths of two sides and the included angle:
Area = 1/2 * BC * CD * sin(B)
First, we need to find the length of side BC using the Pythagorean theorem in triangle ABC:
AC^2 = AB^2 + BC^2
24^2 = 20^2 + BC^2
576 = 400 + BC^2
176 = BC^2
BC = √176 ≈ 13.27 cm
Next, we calculate the length of side CD using the Pythagorean theorem in triangle BCD:
CD^2 = BC^2 + BD^2
CD^2 = 13.27^2 + 15^2
CD^2 = 176.4529 + 225
CD^2 = 401.4529
CD ≈ √401.4529 ≈ 20.04 cm
Now, we find the sine of angle B using the definition of sine in triangle ABC:
sin(B) = opposite/hypotenuse
sin(B) = 15/24
sin(B) = 0.625
Finally, we can calculate the area of triangle BCD:
Area = 1/2 * BC * CD * sin(B)
Area = 1/2 * 13.27 * 20.04 * 0.625
Area ≈ 83.66 cm^2
Therefore, the area of triangle BCD is approximately 83.66 cm^2.