The length of each leg of the given triangle is 13√2, 13√2, and 26 respectively. Using trigonometric ratios the lengths of the triangular legs are calculated using the angles in the triangle.
What are the trigonometric ratios?
The three basic trigonometric ratios are:
Sin A = opp/hyp
Cos A = adj/hyp
Tan A = opp/adj
where A is the acute angle, opp- opposite side of the triangle, adj- adjacent side of the triangle, hyp- hypotenuse of the triangle w. r. t the acute angle.
Calculation:
The given triangle has three angles 45°, 45°, and 90°. The length of the hypotenuse is 26 units.
So, w.r.t the acute angle 45°,
1) Sin 45° = opp/hyp
Since we have Sin 45° = 1/√2 from the trigonometric table,
1/√2 = opp/26
⇒ opp = 26/√2
∴ opposite site length = 13√2 units
2) Cos 45° = adj/hyp
Since we have Cos 45° = 1/√2 from the trigonometric table,
1√2 = adj/26
⇒ adj = 26/√2
∴ adjacent side length = 13√2 units
Therefore, the lengths of each side of the triangle are 13√2, 13√2, and 26 units.
Learn more about trigonometric ratios here:
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