how do i do this question?

a tower stands on top of a cliff. at a distance of 55m from the foot of the cliff, the angles of elevation of the top of the tower as well as the cliff are 60degrees and 45degrees respectively. what is the height of the tower?

Draw a figure. Convince yourself that
Cliff height = 55 tan 45
Cliff height + Tower height = 55 tan 60

Now one bit of subtraction will give you the answer

To solve this question, let's first draw a figure to visualize the given information.

1. Draw a vertical line to represent the cliff.
2. At the base of the cliff, draw a horizontal line to represent the ground.
3. Mark a point on the ground that is 55m away from the base of the cliff.
4. From this point, draw a line at an angle of 45 degrees upwards towards the top of the cliff.
5. Finally, from the top of the cliff, draw a line at an angle of 60 degrees upwards to represent the tower.

Now, let's use some trigonometry to find the height of the tower.

Given that the angle of elevation of the top of the tower is 60 degrees, we can use the tangent function to calculate the height of the tower. Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case, the opposite side is the height of the tower, and the adjacent side is the distance between the base of the cliff and the point 55m away. Therefore, we can write:

tan(60 degrees) = height of tower / 55m

Next, let's calculate the height of the cliff. We know that the angle of elevation of the cliff is 45 degrees. Similarly, we can use the tangent function to find the height of the cliff:

tan(45 degrees) = height of cliff / 55m

Now, we can substitute the values we know into these equations and solve for the heights:

Using the value of the tangent of 60 degrees (approximately 1.732) and the known distance of 55m, we have:

1.732 = height of tower / 55m

Multiplying both sides by 55m:

1.732 * 55m = height of tower

Simplifying:

height of tower ≈ 95.26m

Similarly, using the value of the tangent of 45 degrees (approximately 1), we have:

1 = height of cliff / 55m

Multiplying both sides by 55m:

1 * 55m = height of cliff

Simplifying:

height of cliff ≈ 55m

Now, we can find the height of the tower by subtracting the height of the cliff from the total height:

tower height = tower height + cliff height - cliff height

tower height = 95.26m + 55m - 55m

tower height ≈ 95.26m

Thus, the height of the tower is approximately 95.26m.