Chapter

Chapter 7
Section

Chapter Review on Trigonometry of Right Triangles

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Solutions
43 Videos

Are all circles similar? Justify your reasoning.

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Q2

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

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Q3

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

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Q4

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

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Q5a

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

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Q5b

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

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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.

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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?

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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?

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Q8

Find the measure of `\angle A`

, to the nearest degree.

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Q9a

Find the measure of `\angle A`

, to the nearest degree.

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Q9b

Find `x`

, to the nearest tenth of a centimetre.

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Q10a

Find `x`

, to the nearest tenth of a centimetre.

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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?

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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?

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Q12

What are the following values?

`\tan 0^o`

`\tan 45^o`

`\tan 90^o`

Show your work.

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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?

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Q14

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

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Q15a

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

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Q15b

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

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0.39mins

Q15c

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

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Q15d

Find `x`

, to the nearest tenth of a unit.

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0.33mins

Q16a

Find `x`

, to the nearest tenth of a unit.

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0.39mins

Q16b

Find `x`

, to the nearest tenth of a unit.

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Q16c

Find `x`

, to the nearest tenth of a unit.

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0.38mins

Q16d

Solve `\triangle FGH`

.

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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`

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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?

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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.

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Q20

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

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Q21a

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Q21b

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Q21c

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Q21d

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Q21e

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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?

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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.

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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.

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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?

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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?

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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?

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0.53mins

Q27

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?

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Q28

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?

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Q29