From a tower 36m high situated on one side of a river, the angle of desperation of the opposite side of the river is 25 degree. FInd the width of the river?
Draw a diagram to show the height of the tower (36m), angle of depression (from horizontal)=25°.
So
tan(25°)=36÷width
Solve for wideth.
20
To find the width of the river, we can use trigonometry and the given information.
Let's label the height of the tower as "h" and the width of the river as "w".
We know the height of the tower (h) is 36m and the angle of depression (A) is 25 degrees.
Using the tangent function, we can set up the following equation:
tan(A) = h / w
Plugging in the values we have:
tan(25) = 36 / w
To solve for w, we first need to find the value of tan(25). We can use a calculator or trigonometric table to determine that tan(25) is approximately 0.4663.
Substituting this value back into the equation:
0.4663 = 36 / w
Now, we can solve for w by isolating it on one side of the equation. We can do this by multiplying both sides of the equation by w:
0.4663 * w = 36
Dividing both sides of the equation by 0.4663:
w ≈ 36 / 0.4663
w ≈ 77.215
Therefore, the width of the river is approximately 77.215 meters.