Building A is 40m high.The angle of depression of the top of Building B from the top of A is 26 degrees.if the two buildings are 10m apart,find the height of building B
Draw a diagram. It should be clear that if B is h meters tall,
(40-h)/10 = tan 26°
Factorise 4xy²-x³-yx²+4y³
To find the height of Building B, we can use trigonometric ratios. In this case, we can use the tangent ratio as we have the angle of depression and the length of the adjacent side (the distance between the buildings).
Let's label the height of Building B as 'h'. According to the problem, Building A is 40m high, and the angle of depression from the top of Building A to the top of Building B is 26 degrees. The distance between the buildings is given as 10m.
Using the tangent ratio, we have:
tan(angle) = opposite/adjacent
In this case, the angle is the angle of depression (26 degrees), the opposite side is the height of Building B (h), and the adjacent side is the distance between the buildings (10m).
So we can write:
tan(26 degrees) = h/10
To find the value of h, we rearrange the equation:
h = 10 * tan(26 degrees)
Using a calculator, we find:
h ≈ 4.7446
Therefore, the height of Building B is approximately 4.7446 meters.