Calculate the height of a cliff PQ if the angle of depression from the top of the cliff to a boat R at sea in the same horizontal plane as Q is 42 degrees the boat is 700 meters away from the foot of the cliff

So here is what you know.

You have a right triangle- the adjacent side of the boat to the bottom of the cliff, the right angle going up the cliff, and the hypotenuse of the top of the cliff to the boat.

You know that the angle opposite the right angle is 42 degrees.

You know that the adjacent side is 700 meters.

With that, we can find the height using the tangent. The equation looks something like this:

a/700= Tan 42deg

Calculate the tangent (using a calculator), multiply both sides by 700, and that will give you the height of PQ.

Sitintile senior secondary school is not the subject. A tutor who is in a hurry or bored might just ignore a posting that appears bogus, or maybe posted by someone who cannot follow simple instructions.

Did you draw a diagram? Review your basic trig functions, and you will see that the height h is found using

h/700 = tan 42°

To calculate the height of the cliff, we can use tangent ratio.

Step 1: Draw a diagram.
Draw a horizontal line to represent the horizontal plane. Label one end as P (top of the cliff) and the other end as Q (foot of the cliff). Draw a vertical line downwards from P and label the point where it meets the horizontal line as R (boat at sea). The distance from R to Q is given as 700 meters.

Step 2: Identify the angle of depression.
The angle of depression from P to R is given as 42 degrees. The angle of depression is the angle between the horizontal plane and the line of sight from the top of the cliff to the boat at sea.

Step 3: Use the tangent ratio.
Tangent is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the height of the cliff PQ, and the adjacent side is the distance from Q to R (700 meters).

Using the formula for tangent:
tan(42 degrees) = (height of PQ) / (700 meters)

Step 4: Calculate the height of PQ.
Rearranging the formula, we get:
(height of PQ) = tan(42 degrees) * (700 meters)

Calculating this value:
(height of PQ) ≈ 0.9004 * 700 meters
(height of PQ) ≈ 630.28 meters

The height of the cliff PQ is approximately 630.28 meters.

To calculate the height of the cliff PQ, we can use the trigonometric concept of angle of depression.

Step 1: Draw a diagram based on the given information. Label the points as follows:
- The top of the cliff as P
- The base of the cliff as Q
- The boat at sea as R
- The foot of the cliff as S (where the boat is located)

Step 2: Identify the angle of depression. In this case, the angle of depression is the angle between the line of sight from the top of the cliff to the boat and the horizontal plane. In our diagram, this angle is labeled as ∠RPQ and is given as 42 degrees.

Step 3: Identify the known length. In this case, the known length is the distance between the boat and the foot of the cliff, which is given as 700 meters.

Step 4: Identify the trigonometric relationship. We can use the tangent function to solve for the height of the cliff. The tangent of an angle is equal to the length opposite the angle divided by the length adjacent to the angle.

Step 5: Set up and solve the equation. We can use the tangent function to set up the equation:

tan(∠RPQ) = PQ / QS

Since we are trying to determine the height of the cliff PQ, we rearrange the equation:

PQ = tan(∠RPQ) * QS

PQ = tan(42°) * 700m

Using a calculator, compute the value of the tangent of 42 degrees:

tan(42°) ≈ 0.9004

Now substitute this value into the equation:

PQ ≈ 0.9004 * 700m

PQ ≈ 630.28m

Therefore, the approximate height of the cliff PQ is 630.28 meters.