Question

Form the following figure, find the values of:

1. cos B
2. tan C
3. sin²B + cos²B
4. sin B. cos C + cos B. sin C

Answer 1

Given angle  BAC = 90°

⇒ BC² = AB² + AC²       ...(BC is hypotenuse)

⇒ 17² = 8² + AC²

⇒ AC² = 289 - 64

⇒ AC² = 225

⇒ AC = `sqrt225`

∴ AC = 15

(i) cos B = `"base"/"hypotenuse" = "AB"/"BC" = 8/17`

(ii) tan C = `"perpendicular"/"base" = "AB"/"AC" = 8/15`

(iiii) sin B = `"perpendicular"/"hypotenuse" = "AC"/"BC" = 15/17`

cos B = `"base"/"hypotenuse" = "AB"/"BC" = 8/17`

∴ sin² B+ cos² B = `(("perpendicular")/("hypotenuse"))^2 + (("base")/("hypotenuse"))^2`

= ` (15/ 17)^2 + (8 /17)^2`

= `(225 + 64) / (289) `

= `(289)/(289) `

=  1

(iv) sin B = `"perpendicular"/"hypotenuse" = "AC"/"BC" = 15/17`

cos B = `"base"/"hypotenuse" = "AB"/"BC" = 8/17`

sin C = `"perpendicular"/"hypotenuse" = "AB"/"BC" = 8/17`

cos C = `"base"/"hypotenuse" = "AC"/"BC" = 15/17`

sin B · cos C + cos B · sin C

= ` 15/17. 15/17 + 8/17. 8/17 `

= `( 225 + 64 )/ (289)`

= `(289)/(289)`

= 1