Question

24. Find x.
9
12

please i need help

Answer 1

16

Explanation:

Let the triangle be ABC and the point of intersection D.

Angle ABD = tan^(-1)(9/12) ~ 36.87°

Angle DBC = angle ABC - angle ABD ~ 53.13°

x = 12 × tan(angle DBC) = 16.

Answer 2

`x = 16`

Explanation:

We can solve for x in the given right triangle by creating ratios of side lengths using the similarity property shared by all of the triangles created when dropping a right triangle's altitude (the dotted line).

First, we should solve for the short leg of the largest right triangle by applying the Pythagorean Theorem to the smallest right triangle:

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

where
`a` and
`b` are the triangle's shorter sides, and
`c` is its hypotenuse.

↓ plugging in the given values:
`a = 9`,
`b= 12`

`9^2 + 12^2 = c^2`

↓ simplifying the exponents on the left side

`81 + 144 = c^2`

↓ executing the addition

`225 = c^2`

↓ taking the square root of both sides

`15 = c`

So, the short leg of the largest right triangle is 15.

Using this value, we can create the following ratios:

short leg : long leg

for the smallest triangle 9 : 12

for the middle triangle 12 :
`x`

We can solve for x by equating these ratios:

`(9)/(12) = (12)/(x)`

↓ multiplying both sides by
`x`

`x\cdot (9)/(12) = 12`

↓ multiplying both sides by
`(12)/(9)`

`\boxed{x = 16}`