In the adjoining figure,the parts AC & CB are the part of a minar AC & CB make angle ® & © at the point P. If tan®=1/2, tan©=1/3;find the height of a minar if PB=16metres
To find the height of the minar, we can use the properties of right triangles and the given information.
Let's label the parts of the triangle:
AC = h (height of the minar)
CB = PB = 16 meters
Angle ® = angle APC
Angle © = angle BPC
Given:
tan® = 1/2
tan© = 1/3
PB = 16 meters
Since tan® = opposite/adjacent, we can say that:
AP/CP = 1/2
Similarly, since tan© = opposite/adjacent, we can say that:
BP/CP = 1/3
Using the concept of similar triangles, we can write the following ratio:
AP/PB = AC/CB
Substituting the known values, we get:
(1/2) = h/16
Simplifying the equation, we find:
h = (1/2) * 16
h = 8 meters
Therefore, the height of the minar is 8 meters.
To find the height of the minar, we need to first find the lengths of AC and CB using the given information about the angles and the length of PB.
We are given that tan® = 1/2, which means that the ratio of the length of AC to the length of CP is 1/2. Similarly, tan© = 1/3, which means that the ratio of the length of CB to the length of CP is 1/3.
Let's assume the height of the minar to be h. We can set up the following equations using the given information:
AC/CP = 1/2 ...(1)
CB/CP = 1/3 ...(2)
CB + AC = h ...(3) (as CB + AC gives the total height of the minar)
Since PB = 16 meters, we can also write:
CP + PB = h
From equations (1) and (2), we can find the values of AC and CB in terms of CP:
AC = (1/2)CP ...(4)
CB = (1/3)CP ...(5)
Substituting equations (4) and (5) into equation (3), we get:
(1/2)CP + (1/3)CP = h
Multiplying through by 6 to clear the fractions, we have:
3CP + 2CP = 6h
5CP = 6h ...(6)
Similarly, substituting CP + PB = h into equations (4) and (5), we get:
(1/2)(CP + PB) = (1/3)(CP + PB)
Simplifying, we have:
3(CP + 16) = 2(CP + 16)
3CP + 48 = 2CP + 32
3CP - 2CP = 32 - 48
CP = -16
We have a negative value for CP, which does not make sense in this context. Therefore, our assumption about the height of the minar, h, must be incorrect.
Please recheck the given information or provide any additional details if available.