Triangle ABC has sides of:

AB=25
BC=4
CA=26

Angle B is a Rt. Angle.

What is the approx. measure of Angle A?
How do you find the answer?

Thanks,
Jane

To find the measure of angle A, we can use the properties of a right triangle. In a right triangle, the sum of the measures of the three angles is always equal to 180 degrees.

Since angle B is a right angle (90 degrees), the sum of angles A, B, and C is 180 degrees. Therefore, we have:

A + B + C = 180

Substituting the given values:

A + 90 + C = 180

Now, we need to find the measure of angle C. We can use the Pythagorean theorem, which relates the sides of a right triangle:

AB^2 + BC^2 = CA^2

Substituting the given values:

25^2 + 4^2 = 26^2

625 + 16 = 676

641 = 676

Now, we can find the measure of angle C using the inverse trigonometric functions. Since we know the lengths of the sides BC and CA, we can use the tangent function:

tan(C) = BC / CA

tan(C) = 4 / 26

C = arctan(4 / 26)

Using a scientific calculator or an online calculator, we find that C is approximately 9.6 degrees.

Now, we can substitute the values of B and C into the equation A + 90 + C = 180:

A + 90 + 9.6 = 180

A + 99.6 = 180

Subtracting 99.6 from both sides:

A = 80.4

Therefore, the approximate measure of angle A is 80.4 degrees.