FROM THE TOP OF A VERTICAL CLIFF 200M SEA LEVEL A BOAT WAS SIGHTED AT ANGLE OF 26CELSIUS ?

To solve this problem, you can use basic trigonometry. Here's how you can find the distance between the boat and the base of the cliff:

1. Draw a diagram representing the situation. Label the top of the cliff as point A, the base of the cliff as point B, and the boat as point C.

A (200m)

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C

2. Angle BAC is given as 26 degrees.

3. Use the tangent function to find the distance BC:
tan(angle) = opposite/adjacent
tan(BAC) = BC/AB
tan(26°) = BC/200

4. Rearrange the equation to solve for BC:
BC = 200 * tan(26°)

5. Use a calculator to evaluate the right side of the equation:
BC ≈ 87.6 meters

Therefore, the distance between the boat and the base of the cliff (BC) is approximately 87.6 meters.

To determine the distance between the top of the vertical cliff and the boat, we can use trigonometry.

Firstly, we need to convert the angle from degrees to radians since trigonometric functions in most programming languages work with radians.

To convert an angle from degrees to radians, multiply it by π/180. In this case, the angle is 26 degrees, so the angle in radians is (26 * π) / 180.

Next, we can use the tangent function to find the distance. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side.

In this scenario, the height of the cliff is the opposite side, and the distance to the boat is the adjacent side. We can set up the following equation:

tan(angle) = height / distance

Substituting the given values:
tan((26 * π) / 180) = 200 / distance

Now, we can solve for the distance. Rearranging the equation, we get:

distance = 200 / tan((26 * π) / 180)

Using a calculator or a programming language with trigonometric functions, you can input the equation and calculate the value of the distance.

Note: π is a mathematical constant representing the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159.