Given a right-angled triangle abc with a right angle C. Find the angle A if

| January 29, 2021 | education

Given a right-angled triangle abc with a right angle C. Find the angle A if 1) the angle B = 62 degrees. 2) angle B is 40 degrees greater than angle A.

1) First, we find the value of the angle A in the right-angled triangle ABC, if by the condition angle C is right, and angle B is equal to 62 °.
As a rule, the sum of all angles of any triangle is 180 °.
Now we will write ABC for the indicated triangle and calculate.
A + B + C = 180 °.
A = 180 ° – (B + C).
A = 180 ° – (62 ° + 90 °).
A = 180 ° – 152 °.
A = 28 °.
Answer: 28 °.
2) Now we find the value of the angle B, if the angle B is greater than the angle A by 40 °.
Let’s assume that the angle A is x degrees.
Then the angle B is equal to (x + 40) degrees.
Now we will write ABC for the indicated triangle and calculate.
In this case, for convenience, we will omit the designation of degrees.
A + B + C = 180.
x + x + 40 + 90 = 180.
2x + 130 = 180.
2x = 180 – 130.
2x = 50.
x = 50: 2.
x = 25 ° – angle value A.
x + 40 ° = 25 ° + 40 ° = 65 ° – angle B.
Answer: 65 °.



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