Triangle trig

[peep1963]

Here's the problem. It should be easy but I can't figure it out.

A rectangle is 14cm wide and 48cm long. Find the measures of the acute angle between the diagonals.


I know that the rectangle makes a 90 degree angle. So therefore both diagonals must be 50cm. The acute angle is the one with 14 as its side. But how do you find that angle? Can you assume that the two bottom angles are 45 degrees? I know that the answer is 32.5. And I can't get that.

Please help.

 

[TchrWill]

Here's the problem. It should be easy but I can't figure it out.

A rectangle is 14cm wide and 48cm long. Find the measures of the acute angle between the diagonals.

I know that the rectangle makes a 90 degree angle. So therefore both diagonals must be 50cm. The acute angle is the one with 14 as its side. But how do you find that angle? Can you assume that the two bottom angles are 45 degrees? I know that the answer is 32.5. And I can't get that.

The diagonal makes an angle µ with the 14cm side.

The ange µ is arctan = 24/7 = 73.739º

The half lengths of the diagonals make an isosceles triangle with the 14cm side.

The two base angles of 73.739º add up to 147.479º.

Therefore, the acute angle between the diagonals is 180 - 147.479 = 32.52º.