Question

The area of a right angled triangle abc is 36cm^2 and also anglea=37degree.find the length of the hypotenuse.

Answer 1

Topic - Trigonometry

Given that, ΔABC is a right-angled triangle.

Its base is AB, height is BC and hypotenuse is AC.

Given, area of ΔABC = 36 cm²

⇒ 1/2 * AB * BC = 36

⇒ AB * BC = 72 .....(i)

Now, BC / AB = tan37°

⇒ 72 / AB² = tan37°

⇒ AB² = 72 / tan37°

⇒ AB = √(72 / tan37°)

Again, AB / AC = cos37°

⇒ √(72 / tan37°) / AC = cos37°

⇒ AC = √(72 / tan37°) / cos37°

⇒ AC = 12.24

Therefore the length of the hypotenuse is 12.24 cm.