An observer on top of a cliff 25m above sea level views a boat on the sea at an angle of depression of 35. How far is the boat from the foot of the cliff?
right-angled triangle trig:
tan35° = 25/x
x = 25/tan35 = appr 35.7 m
hey can you explain please step by step i'm really sorry but i really need your help
wfew
To find the distance from the boat to the foot of the cliff, we can use trigonometry. Let's label the distance from the boat to the foot of the cliff as x.
Given that the observer is 25m above sea level and the angle of depression is 35 degrees, we can form a right triangle. The vertical leg of the triangle represents the height of the cliff (25m), the horizontal leg represents the distance from the boat to the foot of the cliff (x), and the angle of depression (35 degrees) is the angle between the horizontal leg and the hypotenuse.
Using the tangent function, which is given by the formula tan(theta) = opposite/adjacent, we can relate the angle of depression to the sides of the triangle:
tan(35 degrees) = opposite/adjacent
tan(35 degrees) = 25/x
Now, we can solve for x by rearranging the equation:
x = 25 / tan(35 degrees)
Using a calculator, we can find the value of tan(35 degrees) ≈ 0.7. Now we can calculate the value of x:
x = 25 / 0.7 ≈ 35.71 meters
Therefore, the boat is approximately 35.71 meters from the foot of the cliff.