PLEASE HELPPP WILL GIVE BRAINLIEST As the students were approaching the park, they noticed a huge tower that was just being completed. Lucas and Jacob were part of the group responsible for looking at advertising. They couldn't help but to think that one of the main attractions of the park would be the ride involving this tower. It was a bright, sunny day. As they got off the bus, they collected the mathematical materials provided by their teacher. These materials included: pencil, paper, eraser, calculator, measuring tape, a clinometer (a tool used to measure vertical angles). They walked through the park until they reached the shadow of the tower. They looked up and couldn't believe how high it was. Explain how the height of the tower might be calculated from the materials they have, using similar triangles.
If they are going to advertise the height of the tower in a brochure that is being created, they want to be sure of their answer. Describe how they could use the materials they have and trigonometry to determine the height of the tower.

a) By multiplying   the length of the shadow of the tower to the ratio of the height of the exposed pencil placed in the ground to the length of the  pencil's shadow the height of the tower can be found

b) Height of the tower = Level to which the clinometer was raided + length of the shadow of the tower × tan (Angle of elevation of the top of the tower)

Step-by-step explanation:

a) The steps to measure the length of height of the tower using similar triangles are as follows;

Whereby the ground over which the tower is located is flat, place the pencil in the ground and ensure that it is upright and standing on its own

1) Measure the length of the shadow of the pencil

2) Measure the height of the exposed (above the ground) pencil

3) Find the ratio of the height of the exposed pencil to the length of the  pencil's shadow

4) Measure the length of the shadow of the tower

5) Multiply the length of the shadow of the tower to the ratio of the height of the exposed pencil to the length of the  pencil's shadow to find the height of the tower

b) To measure the height of the tower by trigonometry and the materials they have, we have;

1) Measure the length of the shadow of the tower using the measuring tape. Record the length as l

2) From the end of the length of the shadow of the tower, measure the angle of elevation of the top of the tower using the clinometer. Record the angle of elvation as θ

3) Measure the distance from the ground the clinometer was raised to measure the height of the shadow and record it as H₁

The height of the tower can then be found by the following formula;

Height of the tower, h = H₁+ length of the shadow of the tower × tan(θ)

h = H₁ + l × tan(θ)

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