Question

Please help me work through this math problem, much appreciated!

Answer 1

Given:

The sides of the right triangle are given as,

`\begin{gathered} a=30.4 \\ c=50.2 \end{gathered}`

The objective is to find the other side and the angles of the right triangle.

Step-by-step explanation:

To find b:

The third side of the right triangle can be calculated using the Pythagorean theorem.

`\begin{gathered} b^2=c^2-a^2 \\ b=\sqrt[]{c^2-a^2}\text{ . . . . . . (1)} \end{gathered}`

On plugging the values of c and a in equation (1),

`b=\sqrt[]{50.2^2-30.4^2}`

On further solving the above equation,

`\begin{gathered} b=\sqrt[]{2520.04-924.16} \\ =\sqrt[]{1595.88} \\ =39.9484668\ldots\ldots \\ \approx39.95 \end{gathered}`

Thus, the side b of the right triangle is 38.95.

To find angle m∠C:

Since the given figure contains a right triangle, the measure of angle m∠C will be 90°.

To find angle m∠A:

The measure of angle m∠A can be calculated using the trigonometric ratio of sin.

`\begin{gathered} \sin A=(a)/(c) \\ A=\sin ^(-1)((a)/(c))\text{ . . . . . .(2)} \end{gathered}`

On plugging the obtained values in equation (2),

`\begin{gathered} A=\sin ^(-1)((30.4)/(50.2)) \\ =37.27042\ldots\text{..} \\ \approx37.3\degree \end{gathered}`

To find angle m∠B:

Using the angle sum property of the right triangle, the measure of angle B can be calculated as,

`\begin{gathered} A+B+C=180\degree \\ B=180\degree-A-C\text{ . . . . (3)} \end{gathered}`

On plugging the obtained values in equation (3),

`\begin{gathered} B=180-37.3-90 \\ B=52.7\degree \end{gathered}`

Hence, the sides and the angles of the right triangle are,

a = 30.4

b = 39.95

c = 50.2

m∠A = 37.3°

m∠B = 52.7°

m∠C = 90°