Question

13.Tumpale whose eye level is 182 cm tall observes the angle of elevation to

the top of his house to be 32°from her eye level at point A. He walks 20 m
towards the house on a straight line to a point B at which she observes the
angle of elevation of the top of the building to be 40°. Calculate;
a.Distance of A from the house.

Answer 1

To calculate the distance of point A from the house, we can use trigonometric ratios and the given information.

Let's denote the distance from point A to the house as "x."

From point A, Tumpale observes an angle of elevation of 32° to the top of the house. This means that the vertical height from point A to the top of the house is given by:

Height from A = x * tan(32°)

After walking 20 meters towards the house, Tumpale reaches point B. From point B, the angle of elevation to the top of the house is 40°. The new vertical height from point B to the top of the house is given by:

Height from B = (x - 20) * tan(40°)

Since the height of the house remains the same, we can equate the two heights:

x * tan(32°) = (x - 20) * tan(40°)

Now, we can solve this equation to find the value of x, which represents the distance of point A from the house.