In triangle ABC, <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
c^2= a^2+b^2
19^2 = 3^2+b^2
361= 9+b^2
b= √352 = 18.8
what should I do for the next steps?
you have the hypotenuse and the side lengths
use trig functions to find the two unknown angles (A and B)
S-O-H-C-A-H-T-O-A
To find the remaining angles in triangle ABC, you can use the trigonometric ratios. In a right triangle, the three main trigonometric ratios are sine, cosine, and tangent.
Given that angle C is a right angle (90 degrees), we can refer to the remaining angles as angle A and angle B.
To find angle A, you can use the inverse trigonometric function "sine." The sine function is defined as the opposite side divided by the hypotenuse.
sin(A) = opposite/hypotenuse
In this case, the opposite side to angle A is side b, and the hypotenuse is side c.
sin(A) = b/c
Substituting the known values into the equation, we have:
sin(A) = 18.8/19
Now, to find angle A, you can take the inverse sine (sin^-1) of both sides:
A = sin^-1(18.8/19)
Using a calculator, you can find the value of A to the nearest tenth.
To find angle B, you can use the fact that the sum of the angles in a triangle is always 180 degrees:
angle A + angle B + angle C = 180
Since angle C is 90 degrees, we can substitute the known values and solve for angle B:
A + B + 90 = 180
B = 180 - A - 90
Once you have the values of angles A and B, you have found all the remaining angles in the triangle.
Hence, to summarize the steps:
1. Use the equation sin(A) = b/c to find angle A.
2. Take the inverse sine (sin^-1) of both sides to find the value of angle A to the nearest tenth.
3. Use the equation B = 180 - A - 90 to find angle B.
4. Add angles A, B, and 90 degrees to ensure they sum up to 180 degrees.
5. Round your answers to the nearest tenth.