Exam-Style Question on Trigonometry Finance
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 13. This question is similar to one that appeared on an IB Studies paper in 2011. The use of a calculator is allowed.
Christine owns a four sided piece of land shown in the diagram below as ABCD. The length of BC is 180 m, the length of CD is 70 m, the length of AD is 90 m, the size of angle BCD is 82° and the size of angle BAD is 102°. The diagram is not to scale
Christine decides to sell the triangular portion of land ABD. She first builds a straight fence from B to D.
(a) Calculate the length of the fence.
The fence costs 19 USD per metre to build.
(b) Calculate the cost of building the fence. Give your answer correct to the nearest USD.
(c) Show that the size of angle ABD is 28.6°, correct to three significant figures.
(d) Calculate the area of triangle ABD.
She sells the land for 110 USD per square metre.
(e) Calculate the value of the land that Christine sells. Give your answer correct to the nearest USD.
Christine invests 200 000 USD from the sale of the land in a bank that pays compound interest compounded annually.
(f) Find the interest rate that the bank pays so that the investment will double in value in 12 years.
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
©1997 - 2021 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/