# How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a = 7, b = 24, c = 25?

**Solution:**

Given, a right triangle ABC

C is the right angle.

Opposite, a = 7

Adjacent, b = 24

Hypotenuse, c = 25

We have to find the values of all six trigonometric functions.

sin A = opposite/hypotenuse = 7/25

cos A = adjacent/hypotenuse = 24/25

tan A = opposite/adjacent = 7/24

cosec A = 1/sin A = 1/(7/25) = 25/7

sec A = 1/cos A = 1/(24/25) = 25/24

cot A = 1/tan A = 1(7/24) = 24/7

Therefore, the values of six trigonometric functions are sin A = 7/25, cos A = 24/25, tan A = 7/24, cosec A = 25/7, sec A = 25/24 and cot A = 24/7.

## How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a = 7, b = 24, c = 25?

**Summary:**

The values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a = 7, b = 24, c = 25 are sin A = 7/25, cos A = 24/25, tan A = 7/24, cosec A = 25/7, sec A = 25/24 and cot A = 24/7.

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