Question

In △ABC, m∠ACB=90°, m∠ACD=60°, CD is the altitude to AB , and BD = 5 cm. Find AD.

Answer 1

Answer:

5cm

Step-by-step explanation:

Find the diagram attached.

From ΔBCD, ∠BCD = 90-∠ACD

∠BCD = 90-60

∠BCD = 30°

Also tan60 = CD/BD

tan 60 = CD/5

CD = 5tan60

CD = 5√3 cm

Similarly from ΔACD, tan30 = CD/AD

tan30 = 5√3/AD

AD = 5√3/tan30

AD =  5√3/(1/√3)

AD = 5√3 * √3/1

AD = 5 cm

Hence the length of side AD is 5cm