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.