Question

When the angle of elevation of sun changes from 45° to 60°, the length
of shadow of a tower changes to 4 metre. What is the height of the
tower?​

Answer 1

Answer:

70.98 meters High

Step-by-step explanation:

CD is the tower , shadow of which is BC when sun makes an angle CBD=60° ,and shadow AC when sun makes angle BAD=45° ,. SO increase in length of the shadow AB= 30m.

cot45=AC/CD, cot 60=BC/CD

(AC/CD) - (BC/CD) = cot45 - cot60

(AC-BC)/CD =1- (1/√3)

AB/CD =(√3–1)/√3 = 0.732/1.732

1.732 AB =0.732 CD

CD =(1.732/0.732)*30 = 70.98m

The tower is 70.98m high

Answer 2

CD is the tower , shadow of which is BC when sun makes an angle CBD=60° ,and shadowAC when sun makes angle BAD=45° ,. SO increase in length of the shadow AB= 30m.

cot45=AC/CD, cot 60=BC/CD

(AC/CD) - (BC/CD) = cot45 - cot60

(AC-BC)/CD =1- (1/√3)

AB/CD =(√3–1)/√3 = 0.732/1.732

1.732 AB =0.732 CD

CD =(1.732/0.732)*4

CD = 9.46 m

The tower is 9.46 m high