Question

Find the lengths for the missing sides if side a is opposite angle A, side b is opposite angle B and side c is the hypotenuse. If a value is not an integer then type it as a decimal rounded to the nearest hundredth.tan(A)= 100, b=100side a = Answerside c = Answer

Answer 1

Side a = 10,000

Side c = 10,000.5

Step-by-step explanation:

Let's make a diagram of the triangle:

We know:

`\begin{gathered} \tan A=100 \\ b=100 \end{gathered}`

The tan ratio of the angle A is:

`\tan A=(a)/(b)`

Then, we can write:

`\tan A=(a)/(b)=100,b=100`
`(a)/(100)=100`
`a=10,000`

Now that we know the length of the two legs, we can use the pythagorean theorem to find the length of c:

`c^2=a^2+b^2`
`c^2=10,000^2+100^2`

And solve:

`c=√(100,000,000+10,000)=√(100,010,000)=10,000.49999`

To the nearest hundreth, c = 10,000.45