Lesson test: Trigonometry of the right triangle

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Trigonometry of the right triangle

1.[2p]
Why does the sine of an angle not depend on the size of the triangle?

Triangles with the same angles are similar, so their sides are proportional and every ratio is unchanged

Correct

Because the hypotenuse is always $1$

The answer is: Triangles with the same angles are similar, so their sides are proportional and every ratio is unchanged

Because sine is defined only for triangles of unit area

The answer is: Triangles with the same angles are similar, so their sides are proportional and every ratio is unchanged

Because the angle sum is always $180 °$

The answer is: Triangles with the same angles are similar, so their sides are proportional and every ratio is unchanged

2.[1p]
What is $\tan 45 °$ ?

CorrectNot quite: 1

3.[2p]
What is $\cos 30 °$ , to four decimal places?

CorrectNot quite: 0.8660

4.[2p]
A ladder 5.2 m long leans at 68° to the horizontal. How far up the wall does it reach, in metres?

CorrectNot quite: 4.82

5.[3p]
A triangle has $A = 41 °$ , $B = 63 °$ and $a = 12$ . Find $b$ .

CorrectNot quite: 16.30

6.[3p]
Two sides of a triangle are 7 and 9 with an included angle of 52°. Find the third side.

CorrectNot quite: 7.24

7.[3p]
When does the sine rule give two possible triangles?

When two sides and an angle not between them are given

Correct

When all three sides are given

The answer is: When two sides and an angle not between them are given

When two angles and a side are given

The answer is: When two sides and an angle not between them are given

When the triangle is right angled

The answer is: When two sides and an angle not between them are given

8.[2p]
Setting $C = 90 °$ in the cosine rule recovers Pythagoras' theorem.

True

Correct

False

The answer is: True

9.[3p]
Match each set of given data to the rule that solves the triangle.

Two angles and any side
Two sides and the angle between them
Three sides, no angles
One acute angle and one side of a right triangle

the cosine rule
the cosine rule
the sine rule
the basic ratios

Show the answer

Two angles and any side: the sine rule Two sides and the angle between them: the cosine rule Three sides, no angles: the cosine rule One acute angle and one side of a right triangle: the basic ratios

1.[2p] Why does the sine of an angle not depend on the size of the triangle?

2.[1p] What is tan45°?

3.[2p] What is cos30°, to four decimal places?

4.[2p] A ladder 5.2 m long leans at 68° to the horizontal. How far up the wall does it reach, in metres?

5.[3p] A triangle has A=41°, B=63° and a=12. Find b.

6.[3p] Two sides of a triangle are 7 and 9 with an included angle of 52°. Find the third side.

7.[3p] When does the sine rule give two possible triangles?

8.[2p] Setting C=90° in the cosine rule recovers Pythagoras' theorem.

9.[3p] Match each set of given data to the rule that solves the triangle.

1.[2p]
Why does the sine of an angle not depend on the size of the triangle?

2.[1p]
What is $\tan 45 °$ ?

3.[2p]
What is $\cos 30 °$ , to four decimal places?

4.[2p]
A ladder 5.2 m long leans at 68° to the horizontal. How far up the wall does it reach, in metres?

5.[3p]
A triangle has $A = 41 °$ , $B = 63 °$ and $a = 12$ . Find $b$ .

6.[3p]
Two sides of a triangle are 7 and 9 with an included angle of 52°. Find the third side.

7.[3p]
When does the sine rule give two possible triangles?

8.[2p]
Setting $C = 90 °$ in the cosine rule recovers Pythagoras' theorem.

9.[3p]
Match each set of given data to the rule that solves the triangle.