Find x and y for these problems

Problem 4

Explanation:

For any 30-60-90 triangle, the hypotenuse is always double the short leg. The short leg is 5, so that makes the hypotenuse equal to 5*2 = 10

The long leg is equal to sqrt(3) times the short leg. That is how y = 5*sqrt(3)

Problem 5

Explanation:

y = x because the legs of a 45-45-90 triangle are always congruent

Use the pythagorean theorem to find x

a^2+b^2 = c^2

x^2+y^2 = 12^2

x^2+x^2 = 144

2x^2 = 144

x^2 = 72

x = sqrt(72)

x = sqrt(36*2)

x = sqrt(36)*sqrt(2)

x = 6*sqrt(2)

y = x

y = 6*sqrt(2)

A) x = 10 ; y = 5sqrt(3)

B) x = y = 6sqrt(2)

sqrt: square root

Step-by-step explanation:

A) sin(30) = 5/x

½ = 5/x

x = 10

5² + y² = 10²

y²= 75

y = 5sqrt(3)

B) x = y since opposite angles are equal

x² + y² = 12²

x² + x² = 144

2x² = 144

x² = 72

x = 6sqrt(2)

step-by-step explanation:

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