Question

Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find the value of each of the six trigonometric functions of ∅

The length of the missing side of the right triangle is __(?)

Answer 1

Explanation:

Pythagorean theorem is given as

a² +b² = c²

a² = c² - b²

a² = 252 – 202

a² = 625 – 400

a² = 225

a = √225

a = 15

Length of the missing side is 15

To find the value of the six trigonometric function

1) sin x = a/c

= 15/25

sin x = 0.6, x = sin⁻¹ 0.6 = 36.86

2) cos x = b/c

= 20/25

cos x = 0.8, x = cos⁻¹ 0.8 = 36.86

3) tan x = a/b

= 15/20

tan x = 0.75, x = tan⁻¹ 0.75 = 36.86

∴ Θ = 36.86°

4) csc x = c/a

= 25/15

csc x = 1.67 x = csc⁻¹ 1.67

5) sec x = c/b

= 25/20

sec x = 1.25 x = sec⁻¹ 1.25

6) cot x = b/a

= 20/15

cot x = 1.33 x = cot⁻¹ 1.33