Question

ABC is a triangle.
15 cm
10 cm
B
D
12.5 cm
The point Dlles on AC
Angle BDC=90°
BD= 10 cm, AB= 15 cm and DC= 12.5 cm.
(a) Calculate the length of AD.
Give your answer correct to 3 significant figures.

Answer 1

Step-by-step explanation:

Pythagoras for the ABD right-angled triangle (since BD has a 90° with DC, it also has to have a 90° angle with AD) :

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle). a and b being the legs.

in our case :

15² = 10² + AD²

225 = 100 + AD²

125 = AD²

AD = sqrt(125) = 11.18033989... cm

≈ 11.2 cm