Question

What is the length of s

Answer 1

5

Explanation:

You can use Tan(45)=S/5 to solve for S. Tan basically means Opposite/Adjacent. So the opposite side is S and the adjacent side is S. You plug tan(45) into your calc and then multiply it by 5.

Proportion Below

Tan(45)/1 = S/5

You cross multiply to get Tan(45)*5=S

S would be 5

To check you can use the Pythagorean theorem a^2+b^2=c^2

5^2+5^2=

`{5}^(2) + {5}^(2) = √(50)`

25+25=50

Answer 2

You can either solve this with the Pythagorean theorem or the special triangles rule which can be applied to (degrees —>) 45/45/90 or 30/60/90 triangles.

With the Pythagorean theorem: a^2 + b^2 = c^2 is used with the numbers accordingly- 5 and S are legs and can be either a or b while √50 being the hypotenuse can only be c

(5)^2 + (s)^2 =(√50)^2

25 + (s)^2 = 50

√ ((s)^2) = √ (50 - 25)

s = 5

The special Triangles rule actually states that a shortcut can be applied to the corresponding sides (look at picture). S is directly across from a 45 degree angle (and so is 5!)

If a = 5, than s must also = 5.