A tower T is observed from two points A and B which are 240 metres apart. The angle TAB is found to be 57degree and the angle TBA is 78degree. Find the distance of the tower from A.
You say angle TBA = 78°
This is only possible if A and B are on opposite sides of the tower.
Confirm this before I solve it.
A and B are on the opposite side of tower.
To find the distance of the tower from point A, we can use the concept of trigonometry and the given angles.
Let's denote the distance of the tower from point A as h.
Using the tangent function, we can write:
tan(TAB) = h / 240
Since we know the value of the angle TAB (57 degrees), we can substitute it in:
tan(57) = h / 240
Now, we can solve for h by rearranging the equation:
h = tan(57) * 240
Using a calculator, we can calculate:
h ≈ 301.26 meters
Therefore, the distance of the tower from point A is approximately 301.26 meters.
To find the distance of the tower from point A, we can use trigonometry and the given information about the angles and the distance between points A and B.
Let's denote the distance of the tower from point A as "x". Now, we can form a right-angled triangle with sides AB, AT, and BT. Angle TAB is given as 57 degrees, and angle TBA is given as 78 degrees.
First, we can find the angles ATB by subtracting the given angles from 180 degrees:
Angle ATB = 180 - 57 - 78 = 45 degrees
Now, we can apply the tangent function to find the value of x:
tan(ATB) = opposite / adjacent
tan(45) = x / 240
To solve for x, we need to evaluate the tangent of 45 degrees, which is 1:
1 = x / 240
Multiplying both sides of the equation by 240, we get:
240 = x
Therefore, the distance of the tower from point A is 240 meters.