In a ΔABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine
(i) sin A, cos A
(ii) sin C, cos C
Answers
Firstly find the remaining side of the triangle by using Pythagoras theorem (AC² = AB² + BC²), find the trigonometric ratios by using the formula given below :
With reference to ∠A :
Sin A = perpendicular/ hypotenuse = BC / AC
Cos A = base/Hypotenuse = AB/AC
With reference to ∠C :
Sin C = perpendicular/ hypotenuse = AB/AC
Cos C = base/Hypotenuse = BC /AC
SOLUTION :
(i) GIVEN : In Δ ABC , AB= 24 cm , BC = 7cm & ∠ABC = 90°
Now, in Δ ABC,
AC² = AB² + BC²
[By using Pythagoras theorem]
AC² = 24² + 7²
AC² = 576 + 49
AC² = 625
AC = √625
AC= 25
Hypotenuse (AC) = 25
With reference to ∠A :
sinA = Perpendicular /Hypotenuse
sinA= BC/AC
sinA=7/25
cosA = Base /Hypotenuse
cosA = AB/AC
cosA= 24/25
Hence, sin A =7/25, cos A = 24/25
(ii) With reference to ∠C :
sin C = Perpendicular /Hypotenuse
sin C = AB/AC
sin C= 24/25
cos C = Base / Hypotenuse
cos A = BC/AC
cosA = 7/25
Hence, sinA =2 4/25, cosA=7 /25
HPE THIS ANSWER WILL HELP YOU....
Here's the Answer:
•°•°•°•°•°•<><><<><>><><>°•°•°•°•°•
¶¶¶ Points to remember ¶¶¶
¶ According to Pythagoras theorem,
In Right Angled ∆
Hypotenuse² = Opposite² + Adjacent²
¶ sin = Opposite/ Hypotenuse
¶ cos = Adjacent/ Hypotenuse
•°•°•°•°•°•<><><<><>><><>°•°•°•°•°•
Solution :
Given,
In Right Angled ∆ABC,
AB = 24 cm
BC = 7 cm
In ∆ABC,
Hyp = AC
Opp = AB
Adj = BC
•°• AC² = AB² + BC²
=> AC² = 24² + 7²
=> AC² = 625
=> AC = √625 = 25
•°• AC = 25 cm
•°•°•°•°•°•<><><<><>><><>°•°•°•°•°•
(i)
• SinA
=> Sin A = BC/AC
=> Sin A = 7/25
• Cos A
=> Cos A = AB/AC
=> Cos A = 24/25
(ii)
• Sin C
=> Sin C = AB/AC
=> Sin C = 24/25
• Cos C
=> Cos C = BC/AC
=> Cos C = 7/25
Here,
•°• Sin A = Cos C = 7/25
& Sin C = Cos A = 24/25
•°•°•°•°•°•<><><<><>><><>°•°•°•°•°•
©#£€®$
:)
Hope it helps
