Find the value of Sec A. and I have a right triangle BC=30 and BA=34
A)17/8
B)9/17
C)15/17
D)17/15
I chose D
There is missing data here. Is 30 the hypotenuse or one of the legs of the right triangle? The same for 34. There is no way for me to know if BC is one the legs or is BA is the hypotenuse or vice-versa.
Once I know that, I can proceed to help you.
BA is the hypotenuse
BC is the opposite leg
We use the Pythagorean Theorem to find length AC as step 1. In other words, we MUST find the ADJACENT LEG.
AC^2 + BC^2 = BA^2
AC^2 + (30)^2 = (34)^2
AC^2 900 = 1156
AC^2 = 1156 - 900
AC^2 = 256
We now take the square root of both sides of the equation to find AC.
sqrt{AC^2} = sqrt{256}
AC = 16
We now have all three sides.
We need secant.
What is secant?
Secant = hypotenuse/adjacent
Well, 34 is our hypotenuse and we just found AC (our adjacent). See it?
Secant = 34/16
The improper fraction 34/16 = 2_1/8 as a mixed number when reduced to the lowest term.
However, 2_1/8 written as an improper fraction is 17/8.
Final Answer: Choice (A)
Done!
To find the value of sec A, you need to use the given information about the right triangle.
In a right triangle, the secant of an angle A is equal to the ratio of the hypotenuse to the adjacent side. In this case, the hypotenuse is AC, and the adjacent side is BC.
To find the value of sec A, you need to find the length of AC. You can use the Pythagorean theorem: the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, you have BC = 30 and BA = 34. Using the Pythagorean theorem:
AC^2 = BC^2 + BA^2
AC^2 = 30^2 + 34^2
AC^2 = 900 + 1156
AC^2 = 2056
Taking the square root of both sides gives:
AC = sqrt(2056)
AC ≈ 45.36
Now that you have the values of AC and BC, you can find the value of sec A:
sec A = AC / BC
sec A = 45.36 / 30
sec A ≈ 1.512
The correct answer is not provided among the options A, B, C, and D. The correct answer is approximately 1.512.