MATH SOLVE

5 months ago

Q:
# There is a right isosceles triangle. The hypotenuse is 31. Find the value of the two missing legs. Round the answer to the nearest 100th.if possible, I would like to learn the formula for future reference.

Accepted Solution

A:

we know that

A right isosceles triangle has two equal sides and two equal angles

so

has two angles equals to 45°

methodology 1 to solve the problem

Let

x--------> length of the leg of triangle

sin 45°=opposite side/hypotenuse

sin 45°=√2/2

opposite side=hypotenuse*sin 45°------> 31*√2/2---> 21.92 units

methodology 2 to solve the problem

c²=a²+b²

c=hypotenuse------> 31 units

a=leg 1

b=leg 2

a=b

so

c²=2a²------> a²=c²/2------> a²=(31)²/2

a=√[(31)²/2]------> a=31/√2-----> 31√2/2------> 21.92 units

A right isosceles triangle has two equal sides and two equal angles

so

has two angles equals to 45°

methodology 1 to solve the problem

Let

x--------> length of the leg of triangle

sin 45°=opposite side/hypotenuse

sin 45°=√2/2

opposite side=hypotenuse*sin 45°------> 31*√2/2---> 21.92 units

methodology 2 to solve the problem

c²=a²+b²

c=hypotenuse------> 31 units

a=leg 1

b=leg 2

a=b

so

c²=2a²------> a²=c²/2------> a²=(31)²/2

a=√[(31)²/2]------> a=31/√2-----> 31√2/2------> 21.92 units