Question

Find the tangent of the larger acute angle in a right triangle with side lengths 10, 24, and 26.

Tangent of the larger acute angle:

Answer 1

Explanation:

Answer:4/3

Answer 2

The tangent of the larger acute angle in a right triangle with side lengths 10, 24, and 26 is 12/5.

Explanation:

In a right triangle, the hypotenuse (the side opposite the right angle) is the longest side.

Therefore, in a right triangle with side lengths 10, 24, and 26, the hypotenuse measures 26 units and the legs measure 10 and 24 units.

In a right triangle:

• The angle opposite the shortest leg is the smallest acute angle.
• The angle opposite the longest leg is the largest acute angle.

Therefore, the largest acute angle is between the hypotenuse and the shortest leg, which means the side opposite the angle is the longest leg.

The tangent ratio is the ratio of the side opposite the angle to the side adjacent the angle.

Therefore the tangent of the largest acute angle is:

`\implies \sf (O)/(A)=(24)/(10)=(12)/(5)`