Question

Note: Triangle may not be drawn to scale. Suppose a = 7 and c = 12.

Answer 1

To find the missing side in a right triangle, use the Pythagorean Theorem.

Step-by-step explanation:

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

So in this case, if 'a' is 7 and 'c' is 12, we can use the formula a² + b² = c² to find the missing side 'b'.

Substituting the values, 7² + b² = 12². Solving for 'b', we get b = √(144-49) = √95.

Answer 2

To determine the value of b, you can use the Pythagorean theorem:

`c^2=a^2+b^2.`

Substituting a=7, and c=12, you get:

`12^2=7^2+b^2.`

Solving for b, you get:

`\begin{gathered} b^2=12^2-7^2, \\ b=√(144-49), \\ b=√(95). \end{gathered}`

Now, to determine the measures of angles, A, and B, you can use the trigonometric functions sine and cosine:

`\begin{gathered} sinA=(a)/(c), \\ cosB=(a)/(c). \end{gathered}`

Therefore:

`\begin{gathered} A\approx35.7^(\circ), \\ B\approx54.3^(\circ). \end{gathered}`

Answer:

`\begin{gathered} b=9.7, \\ A=35.7^(\circ), \\ B=54.3^(\circ). \end{gathered}`