Pythagoras & Trigonometry Practice Questions

The diagram shows a right-angled triangle.

Work out the length of the side marked $x$.

...................................................... m

Write down the exact value of $\cos 60^\circ$.

Write down the exact value of $\tan 45^\circ$.

In triangle $ABC$, angle $ABC = 90^\circ$ and angle $ACB = 30^\circ$.

$AC = 20$ cm.

Work out the length of $AB$.

Circle the equation that could be used to work out the value of $x$.

$\sin 12^\circ = \dfrac{x}{6.5}$ $\cos 12^\circ = \dfrac{x}{6.5}$ $\cos 12^\circ = \dfrac{6.5}{x}$ $\tan 12^\circ = \dfrac{x}{6.5}$

Work out the value of $x$.

Give your answer correct to 2 decimal places.

$x =$ ......................................................

Work out the size of angle $CAB$.

Give your answer correct to 1 decimal place.

......................................................°

A different rectangle has $AB = 6$ cm and $BC = 11$ cm.

Will the value of $\tan CAB$ increase or decrease?

You must give a reason for your answer.

A straight ladder of length $4.8$ m rests against a vertical wall.

The foot of the ladder is on horizontal ground, $1.4$ m from the base of the wall.

Work out how far up the wall the ladder reaches.

Give your answer correct to 2 decimal places.

...................................................... m

$T$ is a viewing platform at the top of a vertical cliff.

$T$ is $32$ m above sea level.

A boat $B$ is at sea level, $95$ m from the base of the cliff.

Work out the angle of depression of the boat from $T$.

Give your answer correct to 1 decimal place.

......................................................°

Show that this triangle is right-angled.

Work out the area of the triangle.

...................................................... cm$^2$

The diagram shows an isosceles triangle.

Work out the area of the triangle.

...................................................... cm$^2$

$FT$ is a vertical radio mast standing on horizontal ground.

$A$ and $B$ are two points on the ground in a straight line from the foot of the mast, $F$.

$FA = 55$ m.

The angle of elevation of $T$ from $A$ is $40^\circ$.
The angle of elevation of $T$ from $B$ is $25^\circ$.

Work out the value of $x$, the distance $AB$.

Give your answer correct to 1 decimal place.

$x =$ ...................................................... m

$PQRS$ is a trapezium with $PQ$ parallel to $SR$.

Angle $PSR = 90^\circ$ and angle $SPQ = 90^\circ$.

Work out the perimeter of the trapezium.

Give your answer correct to 3 significant figures.

...................................................... m