**PART A: MULTIPLE CHOICE (one (1) mark for each question)**

**For questions 1 to 4, select the best answer.**

**1. **Which is the best estimate for the ration of

cos*q* ?

**A **1.08

**B **2.40

**C **0.38

**D **2.60

- Refer to question 1. Which is the measure of Ð
*q*to the nearest degree?

**A **21º **B **23º **C **47º **D **67º

- Which is the best estimate for the length of
*d*?

**A **3.8 cm **B **4.3 cm** C** 6.0 cm **D **7.1 cm

- Which tool or strategy could you use to solve this triangle?

**A **the sine law** B **the cosine law

**C **the Pythagorean theorem

**D **There is not enough information to solve thistriangle.

MAP4C: Grade 12, Foundations for College Mathematics

**PART C: FULL SOLUTION: For the following questions, show your all work in the space provided.**

- Determine the primary trigonometric ratios for Ð
*q*to three decimal places. (**4 marks)**

- A 16-ft beam is supporting a wall. The beam attaches to the wall 12 ft above the ground. Determine the angle of inclination made by the beam with respect to the ground.
**(3 marks**)

MAP4C: Grade 12, Foundations for College Mathematics

- The point Q(–6, 5) lies on the terminal arm of an angle,
*q*, in standard position.

- Sketch Ð
*q*in standard position.- Determine the primary trigonometric ratios to three decimal places.

**(5 marks)**

- In DCPY,
*c*= 35 km,*p*= 29 km, and*y*= 33 km. Determine the measure of ÐY to the nearest degree. (**4 marks)**

- Two surveyors are 7.7 km apart on a straight highway. They each measure the angle between the highway and a power station and find the angles to be 49º and 60º.

Determine the distance each surveyor is from the power station. (**4 marks)**

MAP4C: Grade 12, Foundations for College Mathematics

- Katie built a simple circuit by connecting a battery to two light bulbs with wire. She took the measurements shown.

Determine the total length of wire used in Katie’s circuit, to the nearest tenth of a centimetre. **(4 marks)**

- Josh wants to replace two guy wires that are supporting a pole. He took measurements and drew this diagram.

**(7 marks)**

- Determine the total length of guy wire that needs to be replaced to the nearest metre.
- Determine the height of the pole to the nearest metre.

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