Question:
Find the values of the sine, cosine, and tangent for ∠A
a. sin A = , cos A = , tan A =
b. sin A = , cos A = , tan A =
c. sin A = , cos A = , tan A =
d. sin A = , cos A = , tan A =
d. sin A = , cos A = , tan A =
Step-by-step explanation:
The triangle for the question has been attached to this response.
As shown in the triangle;
AC = 36ft
BC = 24ft
ACB = 90°
To calculate the values of the sine, cosine, and tangent of ∠A;
i. First calculate the value of the missing side AB.
Using Pythagoras' theorem;
⇒ (AB)² = (AC)² + (BC)²
Substitute the values of AC and BC
⇒ (AB)² = (36)² + (24)²
Solve for AB
⇒ (AB)² = 1296 + 576
⇒ (AB)² = 1872
⇒ AB =
⇒ AB = ft
From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of ft (43.27ft).
ii. Calculate the sine of ∠A (i.e sin A)
The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e
sin Ф = -------------(i)
In this case,
Ф = A
opposite = 24ft (This is the opposite side to angle A)
hypotenuse = ft (This is the longest side of the triangle)
Substitute these values into equation (i) as follows;
sin A =
sin A =
Rationalize the result by multiplying both the numerator and denominator by
sin A =
sin A =
iii. Calculate the cosine of ∠A (i.e cos A)
The cosine of an angle (Ф) in a triangle is given by the ratio of the adjacent side to that angle to the hypotenuse side of the triangle. i.e
cos Ф = -------------(ii)
In this case,
Ф = A
adjacent = 36ft (This is the adjecent side to angle A)
hypotenuse = ft (This is the longest side of the triangle)
Substitute these values into equation (ii) as follows;
cos A =
cos A =
Rationalize the result by multiplying both the numerator and denominator by
cos A =
cos A =
iii. Calculate the tangent of ∠A (i.e tan A)
The cosine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the adjacent side of the triangle. i.e
tan Ф = -------------(iii)
In this case,
Ф = A
opposite = 24 ft (This is the opposite side to angle A)
adjacent = 36 ft (This is the adjacent side to angle A)
Substitute these values into equation (iii) as follows;
tan A =
tan A =