find the measure of each acute angle <A & <B for the right triangle.
a = 26.0 m, b = 65.2 m
sin A = a/c = 26/65.2 = 0.39877,
A = 23.5o.
A + B + C = 180.
23.5 + B + 90 = 180, B = 66.5o.
not helpful
To find the measures of each acute angle in a right triangle, we can use trigonometric ratios such as sine, cosine, and tangent.
In this case, we have the lengths of two sides of the triangle, a = 26.0 m and b = 65.2 m.
We can use the sine ratio, which states that the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, we'll use the side opposite angle A as a and the hypotenuse as b.
sin(A) = O/H
sin(A) = a/b
sin(A) = 26.0/65.2
To find the value of sin(A), we can plug this into a calculator or use a reference table for the values of sine. Let's assume the value of sin(A) as 0.4 (rounded to one decimal place).
sin(A) = 0.4
To find the measure of angle A, we can take the inverse sine (also called arcsine) of 0.4.
A = sin^(-1)(0.4)
Now, we need to calculate the value using a calculator or reference table. Assuming the value of A as 23.6 degrees (rounded to one decimal place).
Similarly, we can find angle B using the other side lengths:
sin(B) = a/b
sin(B) = 26.0/65.2
sin(B) = 0.4
B = sin^(-1)(0.4)
Again, using a calculator or reference table, assuming the value of B as 23.6 degrees (rounded to one decimal place).
So, the measure of each acute angle A and B in the right triangle is approximately 23.6 degrees.