Trigonometry

What is the hypotenuse of a right-angled triangle with sides of $15$ and $20$?

Find the distance from $(0,0)$ to $(-3, 4)$.

In a right-angled triangle, the legs are $1.2\text{ m}$ and $0.5\text{ m}$. What is the hypotenuse?

In a right triangle, if $\cos(A) = 0$, what is the measure of angle $A$?

Calculate $10 \cdot \sin(30^\circ)$.

In a right triangle with hypotenuse $c=13$ and side $a=5$, find the angle opposite side $a$.

Given $a=6, b=8, c=10$, which angle is $90^\circ$?

In $\triangle ABC$, if $a=b=c$, the triangle is:

Find the area of $\triangle DEF$ if $e = 8$, $f = 10$, and $\angle D = 45^\circ$.

Find the area of triangle $PQR$ where $q = 8$ cm, $r = 11$ cm, and $\angle P = 44^{\circ}$.

Two sides of a triangle are 6 cm and 14 cm. The included angle is $82^{\circ}$. Find the area.

In triangle $XYZ$, $x = 20$ cm, $y = 10$ cm, and $\angle Z = 12^{\circ}$. What is the area?

If a ship is traveling on a bearing of $150^{\circ}$ and decides to turn and travel in the exact opposite direction, what is the new bearing?

A vehicle traveling on a bearing of $200^{\circ}$ turns $90^{\circ}$ anticlockwise. What is the new bearing?

A traveler starts at a bearing of $040^{\circ}$ and turns $90^{\circ}$ clockwise. What is the new bearing?

A vertical pole $OP$ of height $12 \text{ m}$ stands at point $O$ on horizontal ground. Point $A$ is $15 \text{ m}$ away from $O$ on the ground. Find the angle of elevation of the top of the pole $P$ from point $A$.

A square-based pyramid has a base side length of $6 \text{ cm}$ and a slant edge (from vertex to base corner) of $10 \text{ cm}$. Calculate the vertical height of the pyramid.

A rectangular cuboid has dimensions $10 \text{ cm} \times 8 \text{ cm} \times 6 \text{ cm}$. What is the length of the internal space diagonal connecting two opposite corners?