Trigonometry - Finding degrees of triangle

[BrownPrincezz]

I'm having problem with this question:

From a point A, three straight lines are drawn to points R, S, T so that TRIANGLE ART is right-angled and points R , S, T are collinear. If AR = 12, AS=13, AT=37, determine the area of TRIANGLE AST.


Is it ok to assume RAS and SAT is 45 degrees?

 

[gradeaswimr]

Is it ok to assume RAS and SAT is 45 degrees?

no. your given 2 sides of triangle ARS find the 3rd side. then notice triangle ART. notice what you're given and determine your goal.

 

[VietDao29]

I'm having problem with this question:

From a point A, three straight lines are drawn to points R, S, T so that TRIANGLE ART is right-angled and points R , S, T are collinear. If AR = 12, AS=13, AT=37, determine the area of TRIANGLE AST.


Is it ok to assume RAS and SAT is 45 degrees?

No, of course, you cannot assume things in mathematics. Everything has to be proven.
Ok AR = 12, AS = 13, and AT = 37, so AR is the smallest of the three.
So if ART is a right triangle, what should be the right angle, then, is it andle A, R, or T?
Knowing the right angle, one can use the Pythagorean theorem, ie: a² + b² = c², where c is the length of the hypotenuse in a right triangle.
You should note that, the area of an triangle ABC can be calculated by:
A = (1 / 2) AH x BC, there AH is its altitude.
Can you go from here? :)

 

[BrownPrincezz]

No, of course, you cannot assume things in mathematics. Everything has to be proven.
Ok AR = 12, AS = 13, and AT = 37, so AR is the smallest of the three.
So if ART is a right triangle, what should be the right angle, then, is it andle A, R, or T?
Knowing the right angle, one can use the Pythagorean theorem, ie: a² + b² = c², where c is the length of the hypotenuse in a right triangle.
You should note that, the area of an triangle ABC can be calculated by:
A = (1 / 2) AH x BC, there AH is its altitude.
Can you go from here? :)

Thank you guys so much :)
That was very helpful