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?

Step-by-step 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

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl