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# how to find area of triangle without height

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Question:I need to know how to find the height a of right angled triangle without measuring it if I know the lengths of the sides. This is so I can work out the area, which I already know how to do, but in some of the problems the height of the triangle isn't given, only the side measurments are. E.g a triangle with sides of 50mm, 13mm and 12mm. How would I work this out? Please explain!!!

Answers:To find the area of a triangle which is not right-angled, when you know only the sides, there are two techniques you can use. Let ABC be the triangle, with sides of length a, b and c opposite angles A, B and C respectively. Drop a perpendicular from B to meet CA at D. Let the length of this perpendicular be h. Method 1: Then in thriangle ABD: h / c = sin(A) h = c sin(A) ................(1) The area S of ABC is: S = bh / 2 ..........(2) Substituting for h from (1) in (2) gives an alternative formula for the area: S = bc sin(A) / 2 ..............(3) As you still need to know sin(A), you can use the cosine rule to find angle A as follows: cos(A) = ( b^2 + c^2 - a^2 ) / 2bc. Once you know cos(A), you can either find A and then its sine, using a calculator, or alternatively use the formula: sin^2(A) = 1 - cos^2(A). Once you know sin(A), you can use (1) above to find h or (2) above to find the area directly. Method 2: There is a more advanced formula for finding the area of the triangle directly from its sides. That is: S = sqrt( s(s - a)(s - b)(s - c) ), where s = (a + b + c) / 2.

Question:I'm in grade 11 math and we've just learned a formula used to calculate the area of a triangle. It's Area=1/2absinC (a and b being two sides and sinC representing an angle) If you've used this formula, how would you solve a triangle with no angle but has three equal sides that are all 54. I know you have to do the inverse somewhere and you're using Sine to find the angle but I'm not quite sure how. Thank you.

Answers:yo do half of base times height so... 27 times 54 witch equals 1458

Question:Please help, I need maths help! I need to know the formula to calculate the perpendicular height of a triangle. thanks Okay, I need to know the FORMULA to calculate the height of a triangle WITHOUT A CALCULATOR. WHAT IS THE FORMULA PLEASE!?

Answers:Area=(base x height)/2 to find the heght you can change the subject and get for height: height=2xArea/base

Question:The three sides of the triangle are 290,940, and 822. How do I find the height to do the area?

Answers:Without a lot of trig, you can't. So use Heron's formula, A = [s(s-a)(s-b)(s-c)] where a, b and c are the sides and s = 1/2 the perimeter