Question

Will give brainiest 100 points
In △RST, what is the length of segment RT? Right triangle RST with RS measuring 16 and angles R and T measure 45 degrees.
8
16radical 2
32
16radical 3

Answer 1

Answer:

$\sf B)\quad \overline{RT} = 16\sqrt{2}$

Step-by-step explanation:

If ΔRST is a right triangle, where angles R and T both measure 45°, then the triangle is a special 45-45-90 triangle.

The measure of the sides of a 45-45-90 triangle are in the ratio 1 : 1 : √2. This means that the length of each leg is equal, and the length of the hypotenuse is equal to the length of a leg multiplied by √2.

In ΔRST, angle S is the right angle, so:

• Leg 1 = RS
• Leg 2 = ST
• Hypotenuse = RT

Given that leg RS measures 16 units, and RT is the hypotenuse, then the length of segment RT is the length of RS multiplied by √2:

$\Large\boxed{\boxed{\sf \overline{RT} = 16\sqrt{2}}}$