PQ is a vertical tower 95m high, the points R and S are on the same horizontal plane as Q, the angle of elevation of P from R is 35 if QS =155m and Q from RQS=48

1.Calculate the distance of QR
2.Calculate the distance of RS
3.Calculate the are of QRS

1. tan35 = 95/QR

QR = 95/tan35 = 136.

2. RS = 155 - QR = 155 - 136 = 19.

3. What do you mean by "the are of QRS"?

To find the answers to these calculations, we can use trigonometric ratios and geometry principles. Let's break down each question one by one:

1. Calculate the distance of QR:
From the given information, we have the height of the tower, PQ, which is 95m. We also know the angle of elevation of P from R, which is 35 degrees. Using this information, we can set up a right-angled triangle with one side being QR (the distance we want to find), the other side being the height of the tower (PQ), and the angle of elevation (35 degrees).

Using the trigonometric ratio tan(theta) = opposite/adjacent, where theta is the angle of elevation and the side opposite to the angle is the height of the tower (PQ), and the side adjacent to the angle is the distance we want to find (QR), we can write it as:

tan(35) = 95/QR

Now, we can solve this equation to find the value of QR:

QR = 95 / tan(35)
QR ≈ 162.45 meters (rounded to two decimal places)

Therefore, the distance of QR is approximately 162.45 meters.

2. Calculate the distance of RS:
We are given that QS = 155m and QR (which we just calculated) is approximately 162.45m. We can calculate the distance of RS by subtracting QR from QS:

RS = QS - QR
RS ≈ 155 - 162.45
RS ≈ -7.45 meters

However, negative distance doesn't make sense in this context, so it seems there is an error in the given information or calculation. Please double-check the values and ensure they are accurate.

3. Calculate the area of QRS:
To find the area of QRS, we need the lengths of both QR and RS. As the second calculation produced a negative result, we cannot determine the area of QRS with the given information. Please double-check the values to ensure accuracy.

In summary:
1. The distance of QR is approximately 162.45 meters.
2. There is an error in the given information or calculation, and the distance of RS cannot be determined.
3. The area of QRS cannot be calculated due to the error mentioned above.