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Solutions
16 Videos

Determine whether the primary trigonometric ratios, the sine law, or the cosine law should be used first to solve each triangle.

**a)**

**b)**

**c)**

**d)**

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0.44mins

Q1

**a)** Find `x`

to the nearest tenth of a centimetre.

**b)** Find `x`

using a different method.

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1.42mins

Q2

**a)** Find `x`

, to the nearest tenth of a centimetre.

**b)** Find `x`

using a different method.

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1.51mins

Q3

While flying at an altitude of `1.5`

km, a plane measures angles of depression to opposite ends of a large crater, as shown. Find the width of the crater, to the nearest tenth of a kilometre.

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1.34mins

Q4

Earth is `149\ 600\ 000`

km from the Sun. This distance is equal to 1 A.U. (astronomical unit). Mars is `1.5`

A.U. from the Sun. One evening, Mars is seen from Earth to make an angle of `68`

`^\circ`

with the Sun.

**a)** Draw a diagram and label the given information.

**b)** How far apart are Earth and Mars at this point, in kilometres?

**c)** Do you think the distance between Earth and Mars is always the same? Explain why or why not.

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2.24mins

Q5

Leia is in a bicycle road race. In the first leg, she rides `12`

km from Riverside to Danton. Then, she turns and rides 17 km to Humberville, making a 74`^\circ`

angle from the first leg. The final turn leads back to Riverside.

**a)** What is the total length of the race, to the nearest kilometre?

**b)** At what angles are the three towns situated with respect to each other? Round to the nearest degree.

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2.12mins

Q6

Trey, who is `1.5`

m tall, is standing at a distance of `14`

m from a building. From his point of view, the bottom and top of the building are separated by 36`^\circ`

, as shown. How tall is the building, to the nearest tenth of a metre?

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1.46mins

Q7

Ron and Ben are two koala bears frolicking in a meadow. Suddenly, a tasty clump of eucalyptus falls to the ground, catching their attention. Ben glances at Ron, who appears to be `15`

m away, then over to the eucalyptus, which appears to be `18`

m away. From Ben's point of view, Ron and the eucalyptus are separated by an angle of `45`

`^\circ`

. Rocco’s top running speed is 1.0 m/s, but Ben can run one and a half times as fast. Can Ben beat Ron to the eucalyptus? State any assumptions you make.

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1.13mins

Q8

Find the total length of materials required to build the bridge truss shown, to the nearest tenth of a metre.

Describe the steps in your solution and state any assumptions you make.

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4.37mins

Q9

Lookout Point is accessible from two trails, both of which start from the same altitude and climb upward. Path p travels east to the point and climbs at an average angle of elevation of 20`^\circ`

. Path q travels northeast to the point at an average angle of elevation of 15`^\circ`

. Path p is 2.0 km long. lack and Debbie parked at the base of path p. They hiked a round trip up path p to Lookout Point. then down path q, and then finally straight from the base of path q back to their truck. How far did they hike, to the nearest tenth of a kilometre? State any assumptions you make.

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3.12mins

Q10

A tetrahedron has edges that are `10`

cm in length. Find the height of this tetrahedron. to the nearest tenth of a centimetre.

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2.39mins

Q11

Doctors Jones and Hwang are astronomers observing the sun from opposite ends of Earth. The radius of Earth is 6400 km.

**a)** Use this information to verify the distance from Earth to the Sun, which
was given in question 5. State any assumptions you make.

**b)** At approximately what times of day were these observations made by each astronomer? Explain your answer.

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1.27mins

Q12

Pilots must take wind into account when flying, or the wind will blow them off course and they will not reach the desired destination. Your aircraft cruises at a speed of 100 km/h. There is a strong wind blowing from N60`^\circ`

E at a speed of 90 km/h. You need to fly south to home base.

**a)** Find the direction, `\theta`

, you must aim the plane. to the nearest degree.

**b)** What will your speed be, over the ground? Round to the nearest unit.

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1.33mins

Q13

Hanna, Jon. and Robin live in two identical apartment buildings. located `30`

in apart. Jon lives two floors higher than Hanna. Robin lives four floors lower than Hanna. There is a 36`^\circ`

angle of separation when Hanna looks from her balcony to those of her two friends.

**a)** How far apart, vertically, do Jon and Robin live? Round to the nearest tenth of a metre.

**b)** Explain how you solved this problem and discuss any assumptions you made.

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1.26mins

Q14

A box is in the shape of a square-based prism. The height of the box is twice the width of the base.

**a)** Show that the longest thin rod that can be encased in the box has length `\sqrt{6}w`

, where `w`

is the width of the base.

**b)** Find the angles that such a rod would make with each edge of the box.

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2.46mins

Q15

A ship travels 100 km at a bearing of N60`^\circ`

E and then turns and travels 80 km at a bearing of S2O`^\circ`

E before reaching its destination. Suppose the ship travelled directly from its starting point to its destination, following a direct route. What distance and at what bearing would the ship travel? Round to the nearest unit.

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3.11mins

Q16

Lectures
5 Videos

`a^2 = b^2 + c^2 -2bc\cos A`

`b^2 = a^2 + c^2 -2ac\cos B`

`c^2 = a^2 + b^2 -2ab\cos C`

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4.42mins

1 Introduction to Cosine Law

*ex* A tunnel is to be built through a mountain. To estimate the length of the tunnel, a surveyor makes the measurements shown in Figure 3. Use the surveyor's data to approximate the length of the tunnel.

The approximate length of the tunnel is 416.8 ft.

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0.34mins

2 SAS Cosine Law ex1

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2.03mins

3 SSS Cosine Law Formula

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2.30mins

5 ex4 Multi Step example

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1.49mins

6 ex5 3 dimension example