In a right tringle ,angle ABC has a value of 37 degree while its opposite side is equal to 5,where angle c=90 degree
Find
A.)Remaining sides of the triangle
B.)Angle ABC using any trigonometry Functions
Check your 4:12am post for solution.
To find the remaining sides of the triangle, we can use the trigonometric ratios sine, cosine, and tangent.
Let's label the sides of the triangle as follows:
- Side AB is the side opposite to angle C and is known to be 5.
- Side BC is the hypotenuse, which is the side opposite to the right angle C.
- Side AC is the side adjacent to angle C.
A.) To find the remaining sides of the triangle:
1. Side AC (opposite to angle B):
We can use the sine function: sin(B) = opposite/hypotenuse
sin(B) = AC/BC
Since angle B is complementary to angle C, B = 90 - C
sin(90 - C) = AC/BC
sin(90 - 37) = AC/BC
sin(53) = AC/BC
AC = sin(53) * BC
AC ≈ 3.97
2. Side BC (hypotenuse):
We already know that BC = 5.
B.) To find angle ABC using any trigonometric functions:
We can use the inverse sine (arcsine) function:
sin(B) = opposite/hypotenuse
sin(B) = AC/BC
B = arcsin(AC/BC)
B = arcsin(3.97/5)
B ≈ 53.13 degrees
Therefore:
A.) The remaining sides of the triangle are:
Side AC ≈ 3.97
Side BC = 5
B.) Angle ABC ≈ 53.13 degrees
To find the remaining sides of the right triangle, we can use the trigonometric ratios sine (sin), cosine (cos), and tangent (tan). These ratios are defined as follows:
1. Sine (sin): Opposite side / Hypotenuse
2. Cosine (cos): Adjacent side / Hypotenuse
3. Tangent (tan): Opposite side / Adjacent side
Let's use the given information to find the values of the remaining sides:
Given:
Angle ABC = 37 degrees
Opposite side (AB) = 5
Angle C = 90 degrees (right angle)
To find the remaining sides:
Step 1: Identify the sides of the triangle
In the right triangle ABC, the side opposite angle ABC is AB, the side adjacent to angle ABC is BC, and the hypotenuse of the triangle is AC.
Step 2: Find the hypotenuse (AC)
Since angle C is a right angle, we can use the Pythagorean theorem to find the hypotenuse (AC):
AC^2 = AB^2 + BC^2
AC^2 = 5^2 + BC^2
AC^2 = 25 + BC^2
Step 3: Find BC
Since we know that angle ABC is 37 degrees, we can use the cosine (cos) ratio to find BC:
cos(ABC) = BC / AC
cos(37°) = BC / AC
BC = cos(37°) * AC
Step 4: Calculate the remaining sides
Now that we have the value of BC, we can substitute it into the equation from step 2 to find AC:
AC^2 = 25 + BC^2
AC^2 = 25 + (cos(37°) * AC)^2
By solving this equation, we can find the value of AC.
To find angle ABC using any trigonometric function, let's use the sine (sin) ratio:
sin(ABC) = AB / AC
By substituting the given values, we can solve for angle ABC.
By following these steps, you can find the remaining sides of the triangle and angle ABC using trigonometric functions.