To find the value of x (AM) in triangles ABC and CAM, we use the Pythagoras' theorem on both right-angled triangles, resulting in the solution x = 18.8, corresponding to option B.
To find the value of x, which is the length of side AM in triangles ABC and CAM with right angles at B and C respectively, we can use Pythagoras' theorem.
This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here, in triangle CAM, we have:
AM2 = AC2 + CM2
Since AB = 49.5 and BM = 60, we can find AC by using triangle ABM (which is also right-angled at B).
AM2 = (AB2 - BM2) + CM2
AM2 = (49.52 - 602) + 162
Calculate this expression to find the value of AM.
Once we solve for AM, we can compare the result to the given options and find that the correct answer is B. 18.8.
The probable question may be:
In triangle ABC and CAM , angle ABC and Angle CAM both are 90 degree each. side AB=49.5, Bm=60, CM=16 , AM=x. Find the value of x.
A. 32
B. 18.8
C. 21.5
D. 18