Pythagoras & Trigonometry Practice Questions

The size of a television screen is the length of its diagonal.

A rectangular television screen is $96$ cm long and $54$ cm high.

Work out the size of this television screen.
Give your answer correct to 1 decimal place.

$PQR$ is a right-angled triangle.

Work out the size of angle $PRQ$.
Give your answer correct to 1 decimal place.

$A$ is the point with coordinates $(1,\,-4)$.
$B$ is the point with coordinates $(7,\,3)$.

Work out the length of $AB$.
Give your answer correct to 3 significant figures.

Work out how far up the wall the ladder reaches.
Give your answer correct to 3 significant figures.

A safety notice says that a ladder is safe to use only when the angle between the ladder and the ground is between $70^\circ$ and $80^\circ$.

Use calculations to decide whether this ladder is safe to use.

A triangle has sides of length $9$ cm, $12$ cm and $15.1$ cm.

Ravi says,

"This triangle must be right-angled."

Is Ravi correct?
You must show how you get your answer.

Work out the distance $FB$.
Give your answer correct to 3 significant figures.

The boat then sails $60$ m directly towards the foot of the cliff, to the point $C$.

Work out the angle of elevation of $T$ from $C$.
Give your answer correct to 1 decimal place.

Show that the perpendicular height of the triangle is $6\sqrt{3}$ cm.

Work out the exact area of the triangle.
Give your answer in the form $k\sqrt{3}$ cm$^2$, where $k$ is an integer.

Work out the size of angle $PQR$.
Give your answer correct to 1 decimal place.

Work out the area of triangle $PQR$.
Give your answer correct to 3 significant figures.

Work out the length of $BC$.
Give your answer correct to 3 significant figures.

Work out the size of angle $BCD$.
Give your answer correct to 1 decimal place.

$ABC$ is a triangle.
$D$ is the point on $BC$ such that $AD$ is perpendicular to $BC$.
$AB = 12$ cm, $DC = 15$ cm and angle $ABD = 52^\circ$.

Work out the perimeter of triangle $ABC$.
Give your answer correct to 3 significant figures.

Show that $AD = 5$ cm.

Work out the exact length of $AC$.
Give your answer in the form $a + b\sqrt{3}$ cm, where $a$ and $b$ are integers.

Work out the exact area of triangle $ABC$.

The diagram shows a regular octagon.
All 8 vertices of the octagon lie on a circle of radius $12$ cm and centre $O$.

Work out the perimeter of the octagon.
Give your answer correct to 3 significant figures.