Chapter Review on Trigonometry of Right Triangles
Chapter
Chapter 7
Section
Chapter Review on Trigonometry of Right Triangles
Solutions 43 Videos

Are all circles similar? Justify your reasoning.

Q2

Name the two similar triangles and explain why they are similar.

Q3

Name the two similar triangles and explain why they are similar.

Q4

The pairs of triangles are similar. Find the unknown side lengths.

Q5a

The pairs of triangles are similar. Find the unknown side lengths.

Q5b

The pairs of triangles are similar. Find the unknown side lengths.

Q5c

The tips of the shadows of a tree and of a metre stick meet at the point X.

The following measurements are taken:

XS = 3.5 m

E8 = 6.5 m

Use this information to find the height of the tree, to the nearest tenth of a metre.

Q6

John's garden is in the shape of a right isosceles triangle with base 3.4 m. If she enlarges her garden to a similar shape whose base is doubled, what will the area of her new garden be?

Q7

Sam wants to find the height of a tree without having to climb it, but it is a cloudy day, so he cannot use shadows. He takes a mirror from his pocket and places it on the ground 7.2 m from the base of the tree. He backs up until he can see the top of the tree in the mirror, a distance of 1.2 m from the mirror. If Sid’s eyes are 1.5 m above the ground, what is the height of the tree?

Q8

Find the measure of \angle A, to the nearest degree.

Q9a

Find the measure of \angle A, to the nearest degree.

Q9b

Find x, to the nearest tenth of a centimetre.

Q10a

Find x, to the nearest tenth of a centimetre.

Q10b

A jet climbs at a steady rate at an angle of inclination of 0.5^o during take-off. What will its height be after a 2.2-km initial ascent at this angle?

Q11

Cory is building a ramp for his school theatre production. It must climb a height of 60 cm and have a slope angle of 10°.

a) Draw a diagram and label the given information.

b) What distance will the ramp run along the floor?

c) What will the distance along the surface of the ramp be?

Q12

What are the following values?

• \tan 0^o
• \tan 45^o
• \tan 90^o

Q13

To avoid damaging a vital organ, a surgeon will fire a laser at an angle to the patient’s skin, to reach a cyst (an abnormal growth). The cyst is 8.2 cm directly below the skin, and the laser is positioned at a distance of 9.6 cm away in order to miss the Vital organ, as shown.

At what angle, \theta, should the surgeon position the laser with respect to the skin's surface?

Q14

Find the measure of both acute angles in each triangle, to the nearest degree.

Q15a

Find the measure of both acute angles in each triangle, to the nearest degree.

Q15b

Find the measure of both acute angles in each triangle, to the nearest degree.

0.39mins
Q15c

Find the measure of both acute angles in each triangle, to the nearest degree.

Q15d

Find x, to the nearest tenth of a unit.

0.33mins
Q16a

Find x, to the nearest tenth of a unit.

0.39mins
Q16b

Find x, to the nearest tenth of a unit.

Q16c

Find x, to the nearest tenth of a unit.

0.38mins
Q16d

Solve \triangle FGH.

Q17

In \triangle TUV, UV = 7.4 km, \angle U = 90^o, \angle T = 38^o

a) Draw the triangle and label the given information.

b) Solve \triangle TUV

Q18

During a football game, Danny, the quarterback, has the football and is facing the other team’s goal line. His receiver, Javier, is about 5.5 m to Danny’s left, at an angle of 30°, as shown.

How far should Danny throw the ball to his receiver, to the nearest metre?

Q19

Rachel is heading due south in her sailboat toward a port. After travelling 12 km, she reaches shore 4 km west of her intended destination, due to the water’s current. By what angle did the current push Rachel off course? Include a diagram in your solution and describe any assumptions you must make.

Q20

Solve the triangle. Round each side length to the nearest tenth of a unit and each angle to the nearest degree.

Q21a

Solve the triangle. Round each side length to the nearest tenth of a unit and each angle to the nearest degree.

Q21b

Solve the triangle. Round each side length to the nearest tenth of a unit and each angle to the nearest degree.

Coming Soon
Q21c

Solve the triangle. Round each side length to the nearest tenth of a unit and each angle to the nearest degree.

Coming Soon
Q21d

Solve the triangle. Round each side length to the nearest tenth of a unit and each angle to the nearest degree.

Coming Soon
Q21e

Solve the triangle. Round each side length to the nearest tenth of a unit and each angle to the nearest degree.

Coming Soon
Q21f

The maximum angle of climb for a certain light aircraft is 9°. A line of electric wires 20 m above the ground is located 120 m from the end of the runway. Will the aircraft clear the wires after take-off?

2.00mins
Q22

A stairway runs up the edge of the pyramid. From bottom to top the stairway is 92 m long.

The stairway makes an angle of 70° to the base edge, as shown. A line from the middle of one of the base edges to the top of the pyramid makes an angle of elevation of 52° with respect to the flat ground. Find the height of the pyramid.

Q23

Kathy is 4 m from the base of a long wooden fence, under which her baseball has just rolled. Kathy estimates that the angle of elevation from where she is to the top of the fence is about 30^o. Kathy thinks she can climb over a fence that is a maximum of 2 m high. Can she climb over the fence, or does she have to go around? Justify your reasoning.

1.20mins
Q24

When a road has a 10\% gradient, it means that the road rises 10 In for every 100 m of horizontal distance travelled. What is the angle of inclination of the road, to the nearest degree?

Q25

If you were in a hot air balloon 500 m above the ground, at what angle of depression would you look at a point on the ground 800 m horizontally from the balloon?

Q26

A flagpole casts a shadow 28 m long when the Sun’s rays make an angle of 25^o with the ground. How tall is the flagpole, to the nearest metre?

The world’s longest escalator is in the subway system in St. Petersburg, Russia. The escalator is 330.7 m long and rises a vertical distance of 59.7 m. What 1is the angle of elevation of the top of the escalator when viewed from the bottom, to the nearest degree?
The world’s longest covered bridge crosses the Saint John River in Hartland, New Brunswick. From two points, X and Y, 100 m apart on the same side of the river, the lines of sight to the far end of the bridge, Z, make angles of 85.6° and 79.8° with the river bank, as shown. What is the length of the bridge, b, to the nearest 10 m?