Question

question 5
10 pts
g.gsr.6.3 (mc)
find the value of y.
image of a right triangle with one leg 14, hypotenuse 50, and the other leg y
options:

• y = 48
• y = 35
• y = 40
• y = 30

question 6
10 pts

Explanation:

Step1: Identify the triangle type

The triangle is a right - triangle (has a right - angle symbol). So we can use the Pythagorean theorem, which states that for a right - triangle with legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, one leg \(a = 14\), the hypotenuse \(c = 50\), and the other leg is \(y\). So we can rewrite the Pythagorean theorem as \(y^{2}+14^{2}=50^{2}\).

Step2: Solve for \(y^{2}\)

First, calculate \(14^{2}=196\) and \(50^{2}=2500\). Then, from \(y^{2}+196 = 2500\), we can find \(y^{2}\) by subtracting 196 from both sides of the equation: \(y^{2}=2500 - 196=2304\).

Step3: Solve for \(y\)

Take the square root of both sides. Since \(y\) represents the length of a side of a triangle, we take the positive square root. \(\sqrt{y^{2}}=\sqrt{2304}\), so \(y = 48\).

Answer:

\(y = 48\) (corresponding to the option "y = 48")