In  , <c is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. Show your work.
a = 3, c = 19
If c is the hypotenuse (opposite the right angle) then
c^2 = a^2 + b^2
or
b^2 = 361 - 9
b = sqrt(352) = 18.8
sin A = a/c
sin B = b/c
Thank you
To find the remaining sides and angles in a right triangle, we can use the Pythagorean theorem and trigonometric functions.
Given that side c is the hypotenuse and side a is one of the legs, we can use the Pythagorean theorem to find the length of the other leg, which we'll call b.
Pythagorean theorem:
a^2 + b^2 = c^2
Plugging in the given values:
3^2 + b^2 = 19^2
9 + b^2 = 361
b^2 = 361 - 9
b^2 = 352
Taking the square root of both sides to solve for b:
b = √(352)
b ≈ 18.8
So, the length of the other leg, b, is approximately 18.8.
To find the remaining angles, we can use trigonometric functions. Since we know the lengths of two sides (a and c), we can use the sine, cosine, or tangent function.
Let's find angle A, which is opposite side a.
Sine function:
sin(A) = opposite/hypotenuse
sin(A) = a/c
Plugging in the values:
sin(A) = 3/19
To find angle A, we can take the inverse sine (arcsin) of both sides:
A = arcsin(3/19)
A ≈ 9.2 degrees
To find the remaining angle, angle B, we can use the fact that the sum of the angles in a triangle is 180 degrees.
B = 90 - A
B ≈ 90 - 9.2
B ≈ 80.8 degrees
So, the remaining sides and angles are:
Side b ≈ 18.8
Angle A ≈ 9.2 degrees
Angle B ≈ 80.8 degrees