A right angle triangle is given with the property a2 –b2 =h2 where a and b are lenghts of legs and h is the lenghth of the height to the hypotenuse. Find measures of the angles.
Answers
Given : A right angle triangle is given with the property a²–b² =h²
where a and b are lengths of legs and h is the length of the height to the hypotenuse.
To Find : measures of the angles.
Solution:
Draw triangle ABC right angled at B and BD ⊥ AC
AB = a , BC = b BD = h
in Right angle triangle ADB
AD² = AB² - BD² ( Pythagoras theorem )
=> AD² = a² - h²
h² = a² - b² given => a² - h² = b²
=> AD² = b²
=> AD = b
in Right angle triangle ABC
Tan A = BC/AB = b/a
in Right angle triangle ADB
cos A= AD/AB =b/a
=> Tan A = cos A =b/a
=> A ≈ 38.17 °
∠C = 90° - 38.17 ° = 51.83°
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