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How do you work out the perimeter and interior angles of a right angle triangle when its height is 7.04 cm greater than its base and has an area of 297.3696 square cm?
Wiki User
∙ 13y ago
First the height and base of the triangle must be found so let the height be (x+7.04) and the base be x:-
1/2*height*base = area
1/2*(x+7.04)*x = 297.3696 cm2
Multiply both sides by 2 and multiply out the brackets:
x2+7.04x = 594.7392
Subtract 594.7329 from both sides thus forming a quadratic equation:
x2+7.04-594.7392 = 0
Solving the above by means of the quadratic equation formula gives x a positive value of 21.12
Therefore: height = 28.16 cm and base = 21.12 cm
Use Pythagoras' theorem to find the third side which will be the hypotenuse:
28.162+21.122 = 1239.04 and the square root of this is 35.2
Therefore the perimeter = 28.16+21.12+35.2 = 84.48 cm
Use any of the trigonometrical ratios to find the interior angle:
tan-1(28.16/21.12) = 53.13010235 or 53 degrees to the nearest degree
Therefore the interior angles are 53 degrees, 37 degrees and 90 degrees
Wiki User
∙ 13y ago
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