How do I do this?
i have a right triangle the is angle a, b, and c.
The hypotenuse is 25, the opposite is 7, and the adjacent is 24.
Secant is the opposite of cosine so on my calculator i put in cos^-1(25/24) (the negative 1 is already there i didn't put it there)
i have a right triangle the is angle a, b, and c.
The hypotenuse is 25, the opposite is 7, and the adjacent is 24.
Secant is the opposite of cosine so on my calculator i put in cos^-1(25/24) (the negative 1 is already there i didn't put it there)
-
Your input of cos^-1(25/24) is telling the calculator to find that angle whose cosine is 25/24.
Now 24/24 > 1. The maximum value of the cosine of any angle is ± 1.
Hence, the calculator complains!
[Incidentally, quote: "Secant is the opposite of cosine" is not correct; secant(B) is the reciprocal of cosine(B).)]
Anyway, what follows may not be the most elegant solution you will be offered, but it will work.
Let the angle in consideration be denoted by B.
Then tan(B) = 7/24 = 0.2917
So tan²(B) = 0.08508
However, sec²(B) ≡ 1 + tan²(B)
Therefore, sec²(B) = 1 + 0.08508 = 1.08508
► So: sec(B) ≡ √sec²(B) = √1.08508 = 1.0417
All of that data entry is very easily and quickly done on a calculator: indeed, I have just done that, as shown above.
Now 24/24 > 1. The maximum value of the cosine of any angle is ± 1.
Hence, the calculator complains!
[Incidentally, quote: "Secant is the opposite of cosine" is not correct; secant(B) is the reciprocal of cosine(B).)]
Anyway, what follows may not be the most elegant solution you will be offered, but it will work.
Let the angle in consideration be denoted by B.
Then tan(B) = 7/24 = 0.2917
So tan²(B) = 0.08508
However, sec²(B) ≡ 1 + tan²(B)
Therefore, sec²(B) = 1 + 0.08508 = 1.08508
► So: sec(B) ≡ √sec²(B) = √1.08508 = 1.0417
All of that data entry is very easily and quickly done on a calculator: indeed, I have just done that, as shown above.
-
you must put 1/[cos^-1(24/25)]