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, 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

Q: 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. The explanations should include a detailed diagram,
clear step by step instructions making use of terminology appropriately
and even examples showing the calculations to be used to determine
the height.

The students could use what they know of triangle rectangles, in the image below you can see the diagram that the students could use to estimate the height of the tower.

First, the students could use the measuring tape to find the distance between the base of the tower and them, this distance is represented with the variable S in the image below.

Now, using the clinometer, they could find the elevation angle between their viewpoint and the tip of the tower. This would be the angle θ in the image (notice that they should do this from the ground).

So at this point, we know one angle and the adjacent cathetus to that angle.

And we want to find the height of the tower, which is the opposite cathetus to the known angle.

Then we can remember the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing these by the things we know:

tan(θ) = H/S

tan(θ)*S = H

Then, by measuring θ and S, we can find the height.

If you want to read more about triangle rectangles, you can see:

b because it contains 40% of the possible results from the random list.  

0,1,2,3 v 4,5,6,7,8,9  

4 integers to 6 integers  

40% success vs 60% fail

step-by-step explanation: