A lighthouse is 10 m high and is situated on a vertical cliff which is 70 m above sea-level.The beam of light from the is 192 m from the foot of the cliff.how long is the beam of light at that instant?
The beam length b is
b^2 = 192^2 + (70+10)^2
b^2=192^2+(70+10)^2
b^2=b^2/^2=80/^2
x=40m
To find the length of the beam of light at that instant, we can make use of Pythagoras' theorem. According to the problem, the distance from the lighthouse to the foot of the cliff is given as 192 m, the height of the lighthouse is 10 m, and the cliff is 70 m above sea level.
Let's consider a right-angled triangle with the hypotenuse being the length of the beam of light. The base of the triangle is the distance from the lighthouse to the foot of the cliff, which is 192 m, and the height of the lighthouse is the perpendicular side.
Using Pythagoras' theorem, we can find the length of the hypotenuse (beam of light) as follows:
Length of beam of light = sqrt((Distance from lighthouse^2) + (Height of lighthouse^2))
= sqrt((192^2) + (10^2))
= sqrt(36864 + 100)
= sqrt(36964)
= 192.09 m (approx)
Therefore, at that instant, the length of the beam of light is approximately 192.09 m.