find the remaining sides and angles for the triangle ABC, if b=48 m<a=36 degrees and angle C is a right angle.
what does angle C equal ?
Huh? I am confused... the problem states that angle C is a right angle... so does that simply mean angle C = 90 degrees?
I'm sure Taylor meant angle B. Triangles have to add up to 180 degrees, so 180 - (36+90) = ANGLE B.
To find the remaining sides and angles for triangle ABC, we can use the properties of a right triangle and the trigonometric functions.
Given information:
Side b = 48 m
Angle a = 36 degrees
Angle C is a right angle (90 degrees)
To find angle C, we know that the sum of the angles in any triangle is 180 degrees. Since we already know angle a and angle C, we can find angle B.
180 degrees = angle A + angle B + angle C
180 degrees = 36 degrees + angle B + 90 degrees
Simplifying the equation, we have:
180 degrees - 36 degrees - 90 degrees = angle B
54 degrees = angle B
So, angle B equals 54 degrees.
To find the remaining side, side a, we can use the trigonometric functions. Since we know the length of side b and the measure of angle a, we can use the sine function.
sin(a) = opposite / hypotenuse
sin(36 degrees) = a / 48 m
To find side a, we rearrange the equation:
a = sin(36 degrees) * 48 m
Using a calculator, we can find the value of sin(36 degrees) ≈ 0.5878.
Therefore, side a ≈ 0.5878 * 48 m ≈ 28.14 m.
To summarize:
- Angle C equals 90 degrees.
- Angle B equals 54 degrees.
- Side a ≈ 28.14 m.