Trigonometry Practice Questions

Work out the height that the ladder reaches up the wall.

The ladder is moved so that its foot is $1.4$ m from the wall.

Work out the angle the ladder now makes with the ground.

The two shorter sides of a right-angled triangle are $24$ cm and $45$ cm.

Work out the length of the hypotenuse.

A right-angled triangle has hypotenuse $6.5$ cm and one other side $2.5$ cm.

Work out the length of the third side.

In triangle $PQR$, angle $Q = 90°$, angle $P = 60°$ and $PQ = 6$ cm.

Write down the length of $PR$.

Work out the exact length of $QR$.

In triangle $XYZ$, angle $Y = 90°$, $XY = YZ$ and $XZ = 14$ cm.

Work out the exact length of $XY$.

Work out the length of $QR$.

Give your answer to 3 significant figures.

Work out the area of the flower bed.

Give your answer to 3 significant figures.

Work out the size of the largest angle of the plate.

Work out the area of the plate.

Give your answer to 3 significant figures.

Work out the size of angle $ABC$.

Work out the length of $AB$.

Work out the length of the diagonal $AG$.

Work out the size of the angle between $AG$ and the plane $ABCD$.

Work out the length of $QR$.

Give your answer to 3 significant figures.

Work out the length of $PR$.

Give your answer to 3 significant figures.

Work out the shortest distance from $O$ to the chord $AB$.

Work out the size of angle $AOB$.

Show that $AX = 13$ cm.

Work out the size of the angle between $VA$ and the base $ABCD$.

Work out the size of the angle between the plane $VBC$ and the base $ABCD$.

Show that $AC = 15$ cm.

Work out the size of angle $FAC$.

Work out the area of triangle $ACF$.

Show that $AC = 8\sqrt{2}$ cm.

Work out the exact length of $BC$.

Give your answer in the form $a\sqrt{2} + b\sqrt{6}$, where $a$ and $b$ are integers.

Work out the length of $AC$.

Give your answer to 3 significant figures.

Work out the total area of the field.

Give your answer to 3 significant figures.