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Solutions
36 Videos

Draw two rectangles that are congruent.

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Q1a

Draw two parallelograms that are similar.

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Q1b

Draw two kites that are congruent.

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Q1c

Draw two hexagons that are similar.

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Q1d

Draw two pentagons that are congruent.

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Q1e

Draw two squares that are similar.

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Q1f

Are all squares similar? Justify your answer.

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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 pair of triangles is similar. Find the unknown side lengths.

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Q5

The pair of triangles is similar. Find the unknown side lengths.

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Q6

The tips of the shadows of a short-wave radio antenna and a 2.5-m tree meet at the point C. The following measurements are taken:

VB = 7.4 m

BC = 3.8 m

Use this information to find the height of the short-wave radio antenna, to the nearest tenth of a metre.

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Q7

Nadine has designed a dock in the shape of a right triangle with side lengths 3 m, 4 m, and 5 m. If he enlarges the dock to a similar shape whose side lengths are doubled, what will the area of the new dock be?

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Q8

Find the tangent of the angle indicated, to four decimal places.

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Q9a

Find the tangent of the angle indicated, to four decimal places.

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Q9b

Find the measure of each angle, to the nearest degree.

`\tan \theta = 0.7128`

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Q10a

Find the measure of each angle, to the nearest degree.

`\tan K = 1.3175`

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Q10b

Find the measure of each angle, to the nearest degree.

`\tan \theta = \dfrac{21}{32}`

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Q10c

Find the measure of each angle, to the nearest degree.

`\tan V = \dfrac{17}{9}`

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Q10d

Find `x`

, to the nearest tenth of a metre.

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Q11a

Find `x`

, to the nearest tenth of a metre.

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Q11b

Find the measure of `\angle B`

, to the nearest degree.

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Q12a

Find the measure of `\angle B`

, to the nearest degree.

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Q12b

The angle of elevation of the top of a sail on a sailboat is `72^{\circ}`

. The horizontal length of the sail is 0.8 m. What is the vertical height of the sail, to the nearest tenth of a metre?

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Q13

Find `\sin \theta`

, `\cos \theta`

, and `\tan \theta`

for each triangle, expressed as fractions in lowest terms.

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Q14a

`\sin \theta`

, `\cos \theta`

, and `\tan \theta`

for each triangle, expressed as fractions in lowest terms.

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Q14b

Find the measure of each angle, to the nearest degree.

`\sin F = 0.8156`

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Q15a

Find the measure of each angle, to the nearest degree.

`\sin U = \dfrac{5}{11}`

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Q15b

Find the measure of each angle, to the nearest degree.

`\cos Z = 0.4923`

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Q15c

Find the measure of each angle, to the nearest degree.

`\cos S = \dfrac{3}{7}`

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Q15d

Find `x`

, to the nearest tenth of a metre.

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Q16a

Find `x`

, to the nearest tenth of a metre.

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Q16b

Solve each triangle. Round side lengths to the nearest tenth of a unit and angles to the nearest degree.

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Q17a

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Q17b

Kevin is standing 15 m from the base of a building. From the point where he is standing, the angle of elevation of the top of the building is `32^{\circ}`

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

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Q18

Denny and Selena are standing at the points A and B on the opposite sides of a hydro pole. From point A the angle of elevation of the top of the hydro pole is `28^{\circ}`

, and from point B the angle of elevation of the top of the hydro pole is `34^{\circ}`

. The hydro pole is 7 m in height. How far apart are Denny and Selena, to the nearest tenth of a metre?

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Q19