in a right triangle ABC, C = 90°, a = 33.6 inches and b = 28.4 inches. Find B. Write your answer in decimal degrees (Round your answer to one decimal place.)
B =
i came up with B=49.8 but that is wrong
Did you take tan B?
tanB = 28.4/33.6 = .845238...
angle B= 40.2°
To find the measure of angle B in a right triangle, you can use trigonometric functions. In this case, you can use the sine function.
The sine of an angle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this triangle, side a is opposite angle A, and side b is opposite angle B. The hypotenuse is side c.
To find angle B, you can use the equation sin(B) = b / c.
To solve for B, you first need to find the length of the hypotenuse. Since we know that C = 90°, we can use the Pythagorean theorem:
c^2 = a^2 + b^2
Substituting the given values, we have:
c^2 = 33.6^2 + 28.4^2
c^2 = 1128.96 + 806.56
c^2 = 1935.52
Taking the square root of both sides, we get:
c = √1935.52
c ≈ 43.99
Now that we have the length of the hypotenuse, we can find the sine of angle B:
sin(B) = b / c
sin(B) = 28.4 / 43.99
To find B, we need to take the inverse sine (also known as arcsine or sin^-1) of sin(B):
B = sin^-1(28.4 / 43.99)
Calculating this in a calculator or using a trigonometric table, we find:
B ≈ 40.7 degrees
Therefore, angle B is approximately 40.7 degrees.