Pythagoras Theorem

If length of $AP$ is given as $x$ and $AB=a,BC=a,CA=b$

Use trigonometry to express $x$ in terms of $A\text{ and }b$. Hence show that $a^2=b^2+c^2-2bc\cos A$ .

If length of $AP$ is given as $x$ and $AB=a,BC=a,CA=b$

Use the Pythagorean theorem to write two expressions for $CP$. Hence show that $b^2-x^2=a^2-(c-x{)}^2$.

Label length $AP$ as $x$. Hence label length $PB$ in terms of $c \text{and} x.$

Copy the triangle $ABC,$ with the altitude through $C$ meeting $AB$ at right angles at point $P.$

Consider a right triangle, given below:

Find the value of $x$.

The sum of acute angles in a right-angled triangle is always equal to _____$°$.

A pole of height $10 \mathrm{m}$ stands in front of a house of height $18 \mathrm{m}$. If the distance between the pole and the house is $15 \mathrm{m}$, then find the distance between their tops in $\mathrm{m}$.

Determine whether or not the triangles with the following sides are right-angled triangle:

$11.2, 7.5, 8.3$

Determine whether or not the triangles with the following sides are right-angled triangle:

$10,10,\sqrt{200}$

Determine whether or not the triangles with the following sides are right-angled triangle:

$10 \mathrm{m} , 24 \mathrm{m} , 26 \mathrm{m}$

Determine whether or not the triangles with the following sides are right-angled triangle:

$9 \mathrm{cm} , 40 \mathrm{cm} , 41 \mathrm{cm}$

Find the length of the unknown side in the following right-angled triangle. Round your answers to $1$ decimal point.      [Enter the value excluding units]

Find the length of the unknown side in the following right-angled triangle. Round your answers to $1$ decimal point.      [Enter the value excluding units]

Find the length of the unknown side in the following right-angled triangle. Round your answers to $1$ decimal point.      [Enter the value excluding units]

Find the length of the unknown side in the following right-angled triangle. Round your answers to $1$ decimal point.      [Enter the value excluding units]

In $\Delta PSR, \angle PSR=90°. Q$ is a point on $RS$ such that $PQ=10 \mathrm{cm}, QS=6 \mathrm{cm}, RQ=9 \mathrm{cm}$. Then, the length of $PR$ is

The hypotenuse of a right-angled triangle is $20 \mathrm{cm}$ and the ratio of its other two sides is $4:3$. The length of the sides are

In $\Delta ABC, \angle A=90°, AB=5 \mathrm{cm}, CA=12 \mathrm{cm}$, then the hypotenuse is equal to

The distance between two pillars of heights $35 \mathrm{m}$ and $50 \mathrm{m}$ is $20 \mathrm{m}$. Find the distance of their tops in $\mathrm{m}$.

A ladder of length $15 \mathrm{m}$ is leaning against a window which is $12 \mathrm{m}$ from the ground. The ladder is placed on the window on the other side of the road which is $9 \mathrm{m}$ from the ground. Find the breadth of the road in $\mathrm{m}$.