Question

A plane flying overhead at night is located by two

searchlights as shown at right. The two
searchlights are 1200 feet apart. Angle A = 72°
and angle B = 77º. How high is the plane?

Answer 1

Explanation:

B

2

3

​

​

Let the distance of two consecutive stones are x, x+1.

In ΔBCD, we have

tan60

o

=

x

h

​

⇒x=

3

​

h

​

.....(i)

In ΔABC, we have

tan30

o

=

x+1

h

​

⇒

3

​

1

​

=

x+1

h

​

⇒

3

​

h

​

+1=

3

​

h ......[from equation (i)]

⇒

3

​

2h

​

=1

⇒h=

2

3

​

​

km

solution