Nigel, his girlfriend and his dog sailed and spotted island A when they were 5km away from the island

The tallest palm tree was observed by Nigel as he looked upward 20°, creating triangle TBN (diagram below) with the palm tree

1.

How high is the palm tree knowing that the boat is at the same level as the base of the tree? i.

Solution:

5 minutes later, Nigel had to look at an 60° angle to see the top of the palm tree, what is the speed of the

boat? Given that the speed formula is

2.

Solution:

Evaluation: In this question, the format is similar to the first question, providing Enough data such as the opposite side (found in the previous question) and the

Evaluation: The question is simple in familiar context and is a level 2 type of question. It is straightforward as the question has provided students with enough information about the triangle including one angle and its adjacent, this would enable to solve the question easily by simply applying the tan rule. The result is rounded up to 3 significant figures based on the IB standard system.

(image not for scale)

A few minutes later, Nigel raises his head again, now the angle of elevation is 48°. What is his distance between the boat and the island now, knowing that TN = 2.45?

ii.

(image not for scale)Solution:

Evaluation: This continues to be a level 2 or 3 question as the problem is similar to the previous question. I also added the value of the hypotenuse and which gives students a choice between using tan and cosine rule or to use the Pythagoras theorem. Since the results are rounded up to 3 significant figures, there is an accuracy error, while using tan rule would give the result of 1.6387… using the Pythagoras theorem would give you a result of 1.6401..

AssignmentThursday, March 28, 20139:54 PM

Math 10 - Trigonometry assignment - Ming Ang 866 Page 1

Evaluation: In this question, the format is similar to the first question, providing Enough data such as the opposite side (found in the previous question) and the new side angle of 60° are provided for students to easily apply the tan rule. The Question is a level 5 as it is a question with familiar context yet challenging due to the new additional requirement of finding the speed of the boat and time conversion. The answers are rounded up to 3 significant figures similar to the question above. In order to get the closest approximation, I could have used fraction while converting 5 minutes into hours, which would give a result of 1/12 hours. The afterward speed calculation would then Result 47.4 km/h without having to round up as when I used the time value of 0.083 hours

Calculate the perimeter of the triangle at the current position. 3.

Solution:

Nigel decided to travel around the island circularly and reach to the point with a radian of

from the

original position. Where is Nigel in degree mode?

i.

Solution:

Evaluation:

How far did he travel? ii.

Nigel's girlfriend takes a pictures of Nigel's dog and the tree (diagram below). The girlfriend notices that the three - herself, the dog and the tree- form an isosceles triangle TDG, with DT = TG. If a perpendicular line h from Nigel to the dog is drawn, with Nigel standing between his girlfriend and the tree in a line at point N. Knowing angle DGT is α, prove that:

4.

Area of DTG =

Solution:

Solution:

Evaluation: The question was a complex one for level 8 which requires students to understand the tan and sine rules in

Evaluation: This question applies the Pythagoras theorem and uses the data obtained from previous questions.

Evaluation: This is a simple question which requires students to convert radians to degrees. Though this is a simple question, many students often don't notice the small details while revising the unit. I would have made this question more complex for students so they would find it more challenging yet useful after solving it.

Evaluation: The question applies the circle theorem by requiring students to find the arc length of the sector or the traveled distance of the boat, with the island being the center. The question is pretty realistic since

Math 10 - Trigonometry assignment - Ming Ang 866 Page 2

Calculate the area of the triangle knowing the outer angle of the vertex is 240° and h is 2km

Solution:

Evaluation: This question is made with the purpose to apply the proved rule on the previous question. Once the students were able to solve the previous question, they could easily apply the formula to this question.

Assignment Evaluation:

The assignment was designed to be done in class for 60-90 minutes approximately. It is relatively short and the timing should be enough for students to reach level 6-7 question at the least. I realized that my assignment had some issue regarding to the way questions were phrased, which can easily cause confusion for students who conduct the test, which was why I created some visuals hoping they would help make the questions more understandable, however, I would definitely try to be more cautious when phrasing questions for the next project.

The assignment was not arranged by levels of difficulties as usual, most of the time it was, apart from part 3, which was expected to be a Level 5-6 and contained an easy level 2 question on converting radians to degrees. This might make the marking process a bit more challenging as it would mean that I had given students an easy bonus for level 5, I believed that I should be more aware of the arrangement of the assignment and clearly sort out the range of questions with different levels of difficulty.

The assignment has covered the majority of what we had learnt in this Trigonometry unit, including Pythagoras theorem, sine cosine and tan rules, area of a triangle, radians and degrees conversion; and explore a new rule in question 8. The test could have been added with other questions to cover the Unit Circle, the Cosine graph or the Sine rule in order to cover the Trigonometry unit more thoroughly.

The assignment does have relation to real life event while students solve questions to find the speed, time conversion, the height and length of different variables such as the palm tree or the distance between the boat to the island, or how tilting Nigel's head at different degrees to see the top of the palm tree would show how close he is to the island, or how high the palm tree is.

requires students to understand the tan and sine rules in order to solve. This is one way that I have found to solve the question, and I believe it's not the only way that the question could be solved, however, I haven't found out the new solutions yet.

Math 10 - Trigonometry assignment - Ming Ang 866 Page 3