Year 9 5.2 Trigonometry Review

For the right-angled triangle shown, which is a correct statement?

• $c^2=5^2+12^2$

• $c^2=5^2-12^2$

• $c^2=12^2-5^2$

• $c^2=5^2\times12^2$

• $\left(5+12\right)^2$

Which of the following is true for this triangle?

• $a=5-4$

• $a^2=5^2-4^2$

• $a^2=5^2+4^2$

• $a=\sqrt{10}$

• $a^2-4^2=5^2$

For the right-angled triangle shown:

• $2x^2=49$

• $7x^2=2$

• $2x^2=7$

• $x^2+7^2=x^2$

• $x^2=\frac{2}{7}$

For the triangle shown:

• $\sin\ \theta\ =\ \frac{a}{b}$

• $\sin\ \theta\ =\ \frac{c}{a}$

• $\sin\ \theta\ =\ \frac{a}{c}$

• $\sin\ \theta\ =\ \frac{b}{c}$

• $\sin\ \theta\ =\ \frac{c}{b}$

The value of cos 46°, correct to four decimal places, is:

• 0.7193

• 0.6947

• 0.594

• 0.6532

• 1.0355

In the diagram, the value of x, correct to two decimal places, is:

• 40

• 13.61

• 4.70

• 9.89

• 6.47

The value of x in the triangle is given by:

• 8 sin 46°

• 8 cos 46°

• $\frac{8}{\cos\ 46\degree}$

• $\frac{8}{\sin\ 46\degree}$

• $\frac{\left(\cos\ 46\degree\right)}{8}$

Which equation could be used to find the value of θ?

• $\theta=\tan\left(\frac{4}{5}\right)$

• $\theta=\tan\ \left(\frac{5}{4}\right)$

• $\tan\ \theta=\ \frac{5}{4}$

• $\sin\ \theta=\frac{4}{5}$

• $\tan\ \theta=\frac{4}{5}$

A ladder is inclined at an angle of 28° to the horizontal. If the ladder reaches 8.9 m up the wall, the length of the ladder correct to the nearest metre is:

• 19 m

• 4m

• 2 m

• 10 m

• 24 m

The value of θ in the diagram, correct to two decimal places, is:

• 0.73°

• 48.19°

• 41.81°

• 33.69°

• 4.181°