Question

I need help please I can’t get the answers to match up

Answer 1

`\begin{gathered} A\text{ = 22.62} \\ c\text{ = 13} \\ \end{gathered}`

Step-by-step explanation:

Here, we want to solve for the missing parts of the triangle

we have the value of a as 5 and b as 12

What we have is a right triangle since one of the internal angles is 90 degrees

We can start by getting the value of c

Mathematically, we can get this by the use of Pythagoras' theorem

c faces the right angle and thus, it is the hypotenuse of the triangle

Mathematically, the square of the length of the hypotenuse equals the sum of the squares of the length of the two other sides of a right anlged triangle

We have this as:

`\begin{gathered} c^2=5^2+12^2 \\ c^2\text{ = 25 + 144} \\ c^2\text{ = 169} \\ c\text{ = }\sqrt[]{169} \\ c\text{ = 13} \end{gathered}`

Now, we need to get the other internal angles

We can use the appropriate trigonometric ratios here

The question specifically asks to get the value of internal angle A

From what we have, A faces a and that makes a the opposite

The trigonometric ratio that compares the opposite and the hypotenuse is the sine

It is the ratio of the length of the opposite to the length of the hypotenuse

Mathematically, we have this as:

`\begin{gathered} \sin \text{ A = }(a)/(c) \\ \\ \sin \text{ A = }(5)/(13) \\ A\text{ =}\sin ^(-1)((5)/(13)) \\ \\ A\text{ = 22.62} \end{gathered}`