a We are given right triangle ABC, and we want to find the value of sin A.
To obtain this, we will use the trigonometric ratio for sine.
sin θ = Opposite/Hypotenuse
In our case, the length of the opposite leg is 15, the length of the hypotenuse is 17, and the angle is A.
sin θ = Opposite/Hypotenuse ⇒ sin A = 15/17
Now, we will find the value as a decimal.
b Now, we want to find the value of sec A. To do so we will use the trigonometric ratio for secant.
sec θ = Hypotenuse/Adjacent
In this case, the length of the adjacent leg is 8, the length of the hypotenuse is 17, and the angle is A.
Next, we can rewrite the trigonometric ratio for secant by substituting these values.
sec θ = Hypotenuse/Adjacent ⇒ sec A = 17/8
Let's find the value as a decimal!
c The next value is cot A. We can find its value by recalling the trigonometric ratio for cotangent.
cot θ = Adjacent/Opposite
We know that the length of the adjacent leg is 8, the length of the opposite leg is 15 and the angle is A.
We can rewrite the trigonometric ratio for cotangent by using these values.
cot θ = Adjacent/Opposite
⇒ cot A = 8/15
The next step will be calculating the value as a decimal.
d We want to find the value of csc B. To do that, we will to use the trigonometric ratio for cosecant.
csc θ = Hypotenuse/Opposite
In this case, the length of the opposite leg is 8, the length of the hypotenuse is 17, and the angle is B.
The next step will be rewriting the trigonometric ratio for cosecant by substituting these values.
csc θ = Hypotenuse/Opposite
⇒ csc B = 17/8
As the last step, we will find the value as a decimal.
e We can find the value of sec B by recalling the trigonometric ratio for secant.
sec θ = Hypotenuse/Adjacent
This time the length of the hypotenuse is 17, the length of the adjacent leg is 15, and the angle is B.
Next, we can rewrite the trigonometric ratio for secant by substituting these values.
sec θ = Hypotenuse/Adjacent
⇒ sec B = 17/15
We will calculate this value as a decimal. Let's do it!
f The last value is tan B. To obtain it, we will use the trigonometric ratio for tangent.
tan θ = Opposite/Adjacent
For this case, the length of the opposite leg is 8, the length of the adjacent leg is 15, and the angle is B.
Now, we can rewrite the trigonometric ratio for tangent by substituting these values.
tan θ = Opposite/Adjacent
⇒ tan B = 8/15
Finally, we will find the value as a decimal.
