Question

Solve the problem below

Answer 1

T = 60 degrees

Explanation:

The dotted line is the height so it is a right angle

We are able to use trig functions since this is a right triangle

cos T = adj side / hyp

cos T = a/b

cos T = 8 sqrt(2) / 16 sqrt(2)

cos T = 1/2

Taking the inverse of each side

cos^-1 ( cosT) = cos^-1 ( 1/2)

T = 60 degrees

Answer 2

`\angle T=60^(\circ)`

Explanation:

In all 30-60-90 triangles, the sides are in ratio
`x:x√(3):2x`, where
`x` is the side opposite to the 30 degree angle and
`2x` is the hypotenuse of the triangle. We know that two right triangles are created on both sides of the rectangle in the center. Notice that
`8√(2)\cdot 2=16√(2)` and since
`16√(2)` is the hypotenuse of the right triangle on the left,
`8√(2)` must be facing the 30 degree angle. Therefore, angle T must be 60 degrees.

Alternatively, the cosine of any angle in a right triangle is equal to its adjacent side divided by the hypotenuse.

Therefore, we have:

`\cos \angle T=(8√(2))/(16√(2)),\\\cos \angle T=(1)/(2),\\\angle T=\arccos((1)/(2)),\\\angle T=\boxed{60^(\circ)}`