Question

If X = 10, find the value of the variable b. If your answer is not an integer, round to 2 decimal places.

Answer 1

10 root 2 = hypotenuse
a = leg

In a 45-45-90 triangle:
hyp divided by root 2 = leg
10 root 2 divided by root 2 equals leg
10 equals leg (a)
a = 10

a = long leg
b = short leg
c = hypotenuse

In a 30-60-90 triangle:
long leg divided by root 3 = short leg
10 / root 3 = short leg
short leg = 5.77 (b)

Hypotenuse = short leg * 2
Hyp = 5.77 * 2 = 11.55 (c)

Check using Pythagorean theorem:
a^2 + b^2 = c^2
10^2 + 5.77^2 = 11.55^2
100 + 33.4 = 133.4
133.4 = 133.4 :)