Question

If the tan of angle x is twenty two fifths and the triangle was dilated to be two times as big as the original, what would be the value of the tan of x for the dilated triangle? Clue: Use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no spaces.

Answer 1

The value of  tanx for the new angle is 20²/₅.

Defining tanx

Let tanx = a/b where

• a = opposite to x and
• b = adjacent to x.

We know that tanx = 20²/₅.

The new triangle

Now, if the triangle is dilated and is two times bigger than its original size, it dimensions double. So, it new dimensions are 2a and 2b where 2a is the opposite to the new angle x and 2b is the adjacent to the new angle x.

Tan of the new angle x

So, the tan of the new angle x is tanx = 2a/2b

= a/b

= tanx

= 20²/₅

So, tanx for the new angle is 20²/₅.

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