Question

Select the correct answer.

What is the value of y in the triangle?

a 30-60-90 triangle with long leg length y and hypotenuse length 6

A.

B.

C.

D.

Answer 1

To find the value of y in the triangle, we can use the Pythagorean theorem. In this case, we have a 30-60-90 triangle with a long leg length y and a hypotenuse length of 6. Solving the equation y^2 + (2y)^2 = 6^2 will give us the value of y, which is approximately 2.68.

Step-by-step explanation:

To find the value of y in the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have a 30-60-90 triangle with a long leg length y and a hypotenuse length of 6.

So, using the Pythagorean theorem, we can write the equation as y^2 + (2y)^2 = 6^2. Solving this equation will give us the value of y.

Expanding and simplifying the equation, we have y^2 + 4y^2 = 36. Combining like terms, we get 5y^2 = 36. Dividing both sides by 5, we find y^2 = 7.2. Taking the square root of both sides, we get y ≈ √7.2, which is approximately 2.68.

Answer 2

Answer: In a 30-60-90 triangle the side opposite the 30 degree angle is half the length of the hypotenuse. The shorter leg is the side opposite the 30 degree angle, therefore the shorter leg = 30/2 = 15

By the Pythagorean theorem

the longer leg = √(30² - 15²) = √(900-225) = √675 = 15√3 ≈ 25.98 units