20 time 1000 time 8898 time 2345 divided by 10

The length of the hypotenuse of a right triangle is 24. If the length of one leg is 8, what is approximate length of the other l

Verdich [7]

Something that a right triangle is characterised by is the fact that we may use Pythagoras' theorem to find the length of any one of its sides, given that we know the length of the other two sides. Here, we know the length of the hypotenuse and one other side, therefor we can easily use the theorem to solve for the remaining side.

Now, Pythagoras' Theorem is defined as follows:

c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Given that we know that c = 24 and a = 8, we can find b by substituting c and a into the formula we defined above:

c^2 = a^2 + b^2

24^2 = 8^2 + b^2 (Substitute c = 24 and a = 8)

b^2 = 24^2 - 8^2 (Subtract 8^2 from both sides)

b = √(24^2 - 8^2) (Take the square root of both sides)

b = √512 (Evaluate 24^2 - 8^2)

b = 16√2 (Simplify √512)

= 22.627 (to three decimal places)

I wasn't sure about whether by 'approximate length' you meant for the length to be rounded to a certain number of decimal places or whether you were meant to do more of an estimate based on your knowledge of surds and powers. If you need any more clarification however don't hesitate to comment below.

4 0

3 years ago

Triangle P Q R is shown. Angle Q R P is a right angle. Angle R P Q is 30 degrees and angle P Q R is 60 degrees. Given right tria

mote1985 [20]

Answer:

The correct option is option (c).

$Sin \ P= \frac {RQ}{PQ}$

Step-by-step explanation:

Right angled triangle:

One angle must be 90° and other two angles are acute angle.
The hypotenuses is the longest side of the triangle and opposite right angle.
It follows the Pythagorean Theorem.

Given that,

∠QRP= 90°, ∠RPQ= 30°, ∠PQR = 60°

we know that,

$sin \theta =\frac{Opposite }{Hypotenuse}$