Question

Please Don't spam.

The area of a right triangle is 50. One of its angles is 45°. Find the lengths of the sides and hypotenuse of the triangle. ​

Answer 1

The triangle is right and the size one of its angles is 45°;

the third angle has a size 45° and therefore the triangle is right and isosceles.

Let x be the length of one of the sides and H be the length of the hypotenuse.

Area = (1/2)x2 = 50 ,

solve for x: x = 10

We now use Pythagora to find H:

x2 + x2 = H2

Solve for H: H = 10 √(2)

Hope it may Help you.✌️

Answer 2

Length of the equal sides is 10, and length of the hypotenuse is 10√2

Given:

The area of a right angled triangle = 50 units

One of its angle = 45°

To find:

Find the lengths of the sides and hypotenuse of the triangle. ​

Solution:

Given Triangle is Right angle triangle which means in triangle one angle must be 90°

given another angle is 45°

then third angle = 180° - (90°+45°)   [ ∵ sum of the angle in triangle = 180° ]

Third angle = 180° - 135° = 45°

The angle of given triangle are 45°, 45° and 90°

Since here two angles are equal

the given triangle must be a Isosceles Right Triangle

The area of a right angle triangle A = ½ a²  

[ where a one of the is equal side of triangle ]

From given data area of triangle = 50 units

⇒  ½ a²  = 50

⇒ a² = 100

⇒ a² = 10²

The length of the equal side = 10 cm

From Pythagorean theorem, In a right angle triangle

Hypotenuse² = side² + side²

⇒ Hypotenuse² = 10² +10²

⇒ Hypotenuse² = 200

⇒ Hypotenuse  = √200 = √2×100 = 10√2

Length of the Hypotenuse = 10√2

Length of the equal sides is 10, and length of the hypotenuse is 10√2

#SPJ2